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Comments (60)
Anonymous
15 February 2011
The question should be changed to ask if they have two children born on Tuesday and if one is a boy for the answer to make sense.
Anonymous
4 May 2011
The answer for the Two Children puzzle is 1/2, as most people guess. The correct answer for the riddle is 14/28=1/2, not 13/27.
Anonymous
23 May 2011
Both cases of the boy being born on a Tuesday are statistically independent. It would only be a valid point if it were impossible for both to be born on a Tuesday.
Anonymous
27 June 2011
The answer regarding the days of the week is incorrect. Being born on a Tuesday and the second being born on a Tuesday are independent events, which affects the probability.
Anonymous
21 July 2011
The statistical analysis assumes that once a boy had been born on Tuesday, that option is removed from the pool. In fact, Tuesday boy is still a possibility, resulting in 14/28 (1/2).
Anonymous
29 July 2011
The answer to the Two Children puzzle entails an inconsistency in interpreting the question. The phrasing suggests that the inquiry is about people having two children, but the interpretation of the probability seems flawed.
Anonymous
9 October 2011
Doesn't the solution posted for puzzle #8 reflect the gambler's fallacy? Knowing that the person has two children, one of whom is a boy born on a Tuesday, means the only relevant thing is whether the second child is a boy or a girl, which is a 50/50 probability.
Anonymous
2 November 2011
I think the answer for the 'Two Children' problem is wrong. The graph misrepresents the data given by the question, as each child needs to be represented separately. This is problematic when both children are born on the same day of the week.
Anonymous
8 December 2011
Question #8 - Two Children is ambiguous. Your solution assumed that the person had AT LEAST one boy born on a Tuesday, but one could also assume EXACTLY one boy born on a Tuesday, which would yield an answer of 12/27.
Anonymous
8 December 2011
Question #8 - Two Children is ambiguous. Your solution assumed that the person had at least one boy born on a Tuesday, which could lead to different interpretations.
Anonymous
11 January 2012
Regarding the difficult 'Two Children' puzzle, I believe the inclusion of a 7-day week is arbitrary. If we had a 10-day week, the answer would be different. The birth conditions of one child should not affect the other.
Anonymous
8 August 2012
Your two children riddle is wrong. It assumes that only one of the two could be a boy born on a Tuesday. If I ask you if one is a boy born on a Tuesday and you have two boys born on a Tuesday, then the answer is yes.
Anonymous
8 August 2012
Your riddle about two children assumes that only one could be a boy born on a Tuesday. If both are boys born on a Tuesday, then the answer is yes, one is indeed a boy born on a Tuesday. This is similar to the coin riddle where one coin is not a nickel, but the other can be.
Anonymous
3 September 2012
Two Children is wrong. It is still 50%. The person making the chart failed to recognize that the bb where both children are born on Tuesday should be counted twice, making the chances 14/28 or 50%.
Anonymous
3 September 2012
In 'Two Children', the probability should indeed be reconsidered. The scenario with both children born on Tuesday should be counted twice, affecting the overall probability.
Anonymous
3 September 2012
Concerning the difficult 'Two children' problem, I was wondering why the order of the births matters. The answer is still counterintuitive and further from one-half if order doesn't matter.
Anonymous
17 October 2012
I call BS on the Two Children one. Once one child is born, the chance of the next one is completely independent. Why does it matter if it is Tuesday? If I picked any other day of the week, would it still be 13/27?
Anonymous
17 October 2012
The Two Children puzzle's logic seems flawed. The chance of the next child being a boy or girl is independent of the first child's gender. The day of the week should not affect the probability.
Anonymous
3 November 2012
The issue is that you have the two children's charts overlapped, which would indicate they are dependent. Because they are overlapped, you are counting the column or row for the child that is already known to be a boy, except for the (Boy,Boy) (Tuesday,Tuesday) square. They are independent knowing one of them is a boy.
Anonymous
7 November 2012
Given the answer you gave, the question should read that you also ask if 'at least one' of their children is a boy born on a Tuesday. If both boys were born on Tuesday, the response to whether one was born on a Tuesday would be no because in fact there were two born on Tuesday.
Anonymous
7 November 2012
The question should clarify if 'at least one' of their children is a boy born on a Tuesday. If both boys were born on Tuesday, the response would be no because there were two born on Tuesday.
Anonymous
4 December 2012
The Two Children puzzle has an error. It's a given that one of the children is a boy, therefore there is a 100% chance that that child is a boy. The only child needed to take into consideration is the unknown because of independent assortment of odds, leading to a 50% chance that the other child is a boy.
Anonymous
4 December 2012
The solution to 'Two Children' is flawed. Given that one child is a boy, the probability of the other child being a boy is 50%, not 100%.
Anonymous
10 December 2012
Your solution is wrong. The answer is indeed 1/2. If their boy born on Tuesday is the first child, then the chance of the second child being a boy is 1/2. If their boy born on Tuesday is their second child, then the chance of the first child being a boy is also 1/2.
Anonymous
10 December 2012
The solution to the problem regarding the two children is incorrect. The probability of the second child being a boy is indeed 1/2, regardless of the day of the week.
Anonymous
5 March 2013
The error in your chart is that you counted the overlapped option only once instead of twice. There are two ways for this to happen, so it has to be counted twice. Using this, 28/56 options would be highlighted on your chart. 1/2 is the correct answer.
Anonymous
5 June 2013
I have a comment on the solution to the 'two children' problem. You state that the probability is 13/27 that the second child is a boy, but this seems doubtful to me. You show that only 13 out of 27 combinations are bb, which seems to be correct initially, but it seems that there are two options for bb.
Anonymous
5 June 2013
The probability of the second child being a boy in the 'two children' problem seems incorrect. The combinations for bb should account for the different outcomes based on the names of the boys, which may not have been fully considered.
Anonymous
18 August 2013
For Puzzle #8, if both children are boys born on Tuesday, you should only count that day once, not twice.
Anonymous
2 December 2013
The two children question has the answer wrong; it is 1 chance in two or 50%. The answer given is incorrect as it appears to ignore the fact that the second son can be born on any day of the week, therefore the day of the week is not a variable and the only factor that changes is whether it is a girl or a boy.
Anonymous
2 December 2013
The two children question has the answer wrong. It is 1 chance in two or 50%, as the second son can be born on any day of the week. The answer given ignores this fact.
Anonymous
19 January 2014
The Two Children solution contains a possibility that would mean both of them were boys born on a Tuesday, but we are told that one of them was born on a Tuesday. I got it wrong anyway.
Anonymous
9 February 2014
Puzzle 8 on the Difficult Logic Puzzles page is incorrect. The question implies that one of them is a boy born on Tuesday, not at least one. This changes the probabilities significantly.
Anonymous
1 April 2014
The probability of having two boys is still 1/2 since these are independent events. The solution provided is for the case where two boys are born on Tuesday, which is not specified in the problem.
Anonymous
7 May 2014
Number 8 on difficult in the logical puzzles section is wrong. The probability you gave for having two boys where one is born on a Tuesday is correct, but that would be in a situation where either the boys weren't born or weren't known about yet.
Anonymous
7 May 2014
The probability calculation for the two boys puzzle is incorrect; given one boy born on a Tuesday, the probability of the other child being a boy is 50%.
Anonymous
8 May 2014
I previously mentioned that the probability for puzzle #8 is wrong; the calculation of 13/27 for having two boys with one born on Tuesday is incorrect.
Anonymous
25 August 2014
The answer for 99 people saved doesn't make sense as it assumes the men in line know who is saved. The question states that any correct answer is unknown to all others. If the hats alternate colors, then everyone dies.
Anonymous
28 October 2014
#8 (Two children) is balderdash. Given a mother has two children, and given one child is a boy, the probability the second child is a boy is in fact 1/2. The graph presented is misleading because it simultaneously considers two possible cases which should be considered independently.
Anonymous
2 December 2014
I think that your "Two Children" problem is misleading. The parent confirms that one boy is born on a Tuesday, but it does not necessarily follow that the second child is not also a boy born on Tuesday.
Anonymous
13 May 2015
I believe you forgot the upper-right hand quadrant of boys born on Tuesday, so the total should be 33 and the probability should be 13/33.
Anonymous
3 October 2015
I think the probability will be 1/2 because the condition of asking if the child was born on Tuesday doesnโt make a difference. The child can be born any day, and it doesn't matter if they are younger or older.
Anonymous
3 October 2015
I believe the probability of the second child being born on a Tuesday is 1/2. The condition of asking if he was born on Tuesday doesn't change the overall probability, as the child can be born any day.
Anonymous
26 October 2015
I believe the puzzle regarding two children, one of which is a boy born on Tuesday, is incorrect. I believe the answer is 1/2, not 13/27. Using the chart, the tile in which the column and row intersect, where both are boys born on Tuesday, should be counted twice.
Anonymous
29 May 2016
On the two children problem: Assuming the parents meant one or two boys born on Tuesday, we can conclude the following: The parents rolled a 14 equal-sided die twice and at least once rolled a 3.
Anonymous
25 June 2016
In your difficult logic puzzles, question 8, you say that the answer is 13/27 possibility. However, I disagree with this. If we don't consider the day of birth, there is a 1/2 chance that a newborn child will be a boy.
Anonymous
25 June 2016
I disagree with the answer of 13/27 for question 8. If we consider the possibility of having two boys without the day of birth, the chance would be 1/4. Knowing one child is a boy changes the calculation.
Anonymous
1 October 2016
The question is incorrect; the state 'BB' has a multiplicity of 2 and thus gives a different probability.
Anonymous
31 January 2017
You have ambiguity in the last question you need to eliminate: 'I ask people at random if they have two children and also if one is a boy born on a Tuesday.' What exactly does the phrase 'if one is a boy' mean?
Anonymous
14 March 2017
The probability question regarding two children and one being a boy born on a Tuesday is intriguing. However, the relevance of the day of the week should be explained further.
Anonymous
15 March 2017
The probability question about two children is interesting, but the specific details about the boy born on a Tuesday can be misleading. It would be helpful to clarify how this affects the overall probability.
Anonymous
8 September 2017
The 'two children' answer is wrong. The boy referenced in the question is either the first or second child, and there's a 50% chance the second child is male in either case.
Anonymous
8 September 2017
The answer to the 'two children' puzzle is incorrect. The boy referenced can only be either the first or second child, leading to a 50% chance for each. The graph's highlighted lines create an impossible instance where the boy is both the first and second child.
Anonymous
29 October 2017
The wording of the Two Children puzzle should be changed to clarify that it refers to children born on Tuesday, not just one being a boy born on Tuesday.
Anonymous
14 September 2018
The solution to the two children riddle is wrong. There's a possibility that both children are boys born on Tuesdays, which isn't accounted for in the solution. The real chance is 14/28 (one half) not 13/27.
Anonymous
14 September 2018
For question #8 "Two Children," the answer should be 1/2, not 13/27. The chart leaves out the "2nd" possibility of a Tuesday/Tuesday birthday scenario, which would make the chances of BB to be 14/28.
Anonymous
12 June 2019
Regarding the difficult "two children" puzzle, I was wondering if you could provide more detail as to the solution. The inclusion of a 7-day week seems arbitrary; if we had a 10-day week, the answer would be 19/39.
Anonymous
12 June 2019
The answer to the Two Children puzzle is incorrect; it should be 1/2 as most people guess. The logic used to arrive at 13/27 is not convincing.
Anonymous
15 May 2024
I think the answer for question #8 (Two Children) is incorrect. We already know that the first child is a boy. So the real question becomes: what is the probability that the second child is a boy? The probability of the second child being a boy is independent from the fact that the first child is a boy born on a Tuesday. Since the chance of giving birth to either sex is equal, the probability of the second child being a boy is 1/2 = 50%.
Anonymous
15 May 2024
I believe the answer to question #8 (Two Children) is incorrect. The probability question regarding having two boys needs clarification.
Comments (60)
The question should be changed to ask if they have two children born on Tuesday and if one is a boy for the answer to make sense.
The answer for the Two Children puzzle is 1/2, as most people guess. The correct answer for the riddle is 14/28=1/2, not 13/27.
Both cases of the boy being born on a Tuesday are statistically independent. It would only be a valid point if it were impossible for both to be born on a Tuesday.
The answer regarding the days of the week is incorrect. Being born on a Tuesday and the second being born on a Tuesday are independent events, which affects the probability.
The statistical analysis assumes that once a boy had been born on Tuesday, that option is removed from the pool. In fact, Tuesday boy is still a possibility, resulting in 14/28 (1/2).
The answer to the Two Children puzzle entails an inconsistency in interpreting the question. The phrasing suggests that the inquiry is about people having two children, but the interpretation of the probability seems flawed.
Doesn't the solution posted for puzzle #8 reflect the gambler's fallacy? Knowing that the person has two children, one of whom is a boy born on a Tuesday, means the only relevant thing is whether the second child is a boy or a girl, which is a 50/50 probability.
I think the answer for the 'Two Children' problem is wrong. The graph misrepresents the data given by the question, as each child needs to be represented separately. This is problematic when both children are born on the same day of the week.
Question #8 - Two Children is ambiguous. Your solution assumed that the person had AT LEAST one boy born on a Tuesday, but one could also assume EXACTLY one boy born on a Tuesday, which would yield an answer of 12/27.
Question #8 - Two Children is ambiguous. Your solution assumed that the person had at least one boy born on a Tuesday, which could lead to different interpretations.
Regarding the difficult 'Two Children' puzzle, I believe the inclusion of a 7-day week is arbitrary. If we had a 10-day week, the answer would be different. The birth conditions of one child should not affect the other.
Your two children riddle is wrong. It assumes that only one of the two could be a boy born on a Tuesday. If I ask you if one is a boy born on a Tuesday and you have two boys born on a Tuesday, then the answer is yes.
Your riddle about two children assumes that only one could be a boy born on a Tuesday. If both are boys born on a Tuesday, then the answer is yes, one is indeed a boy born on a Tuesday. This is similar to the coin riddle where one coin is not a nickel, but the other can be.
Two Children is wrong. It is still 50%. The person making the chart failed to recognize that the bb where both children are born on Tuesday should be counted twice, making the chances 14/28 or 50%.
In 'Two Children', the probability should indeed be reconsidered. The scenario with both children born on Tuesday should be counted twice, affecting the overall probability.
Concerning the difficult 'Two children' problem, I was wondering why the order of the births matters. The answer is still counterintuitive and further from one-half if order doesn't matter.
I call BS on the Two Children one. Once one child is born, the chance of the next one is completely independent. Why does it matter if it is Tuesday? If I picked any other day of the week, would it still be 13/27?
The Two Children puzzle's logic seems flawed. The chance of the next child being a boy or girl is independent of the first child's gender. The day of the week should not affect the probability.
The issue is that you have the two children's charts overlapped, which would indicate they are dependent. Because they are overlapped, you are counting the column or row for the child that is already known to be a boy, except for the (Boy,Boy) (Tuesday,Tuesday) square. They are independent knowing one of them is a boy.
Given the answer you gave, the question should read that you also ask if 'at least one' of their children is a boy born on a Tuesday. If both boys were born on Tuesday, the response to whether one was born on a Tuesday would be no because in fact there were two born on Tuesday.
The question should clarify if 'at least one' of their children is a boy born on a Tuesday. If both boys were born on Tuesday, the response would be no because there were two born on Tuesday.
The Two Children puzzle has an error. It's a given that one of the children is a boy, therefore there is a 100% chance that that child is a boy. The only child needed to take into consideration is the unknown because of independent assortment of odds, leading to a 50% chance that the other child is a boy.
The solution to 'Two Children' is flawed. Given that one child is a boy, the probability of the other child being a boy is 50%, not 100%.
Your solution is wrong. The answer is indeed 1/2. If their boy born on Tuesday is the first child, then the chance of the second child being a boy is 1/2. If their boy born on Tuesday is their second child, then the chance of the first child being a boy is also 1/2.
The solution to the problem regarding the two children is incorrect. The probability of the second child being a boy is indeed 1/2, regardless of the day of the week.
The error in your chart is that you counted the overlapped option only once instead of twice. There are two ways for this to happen, so it has to be counted twice. Using this, 28/56 options would be highlighted on your chart. 1/2 is the correct answer.
I have a comment on the solution to the 'two children' problem. You state that the probability is 13/27 that the second child is a boy, but this seems doubtful to me. You show that only 13 out of 27 combinations are bb, which seems to be correct initially, but it seems that there are two options for bb.
The probability of the second child being a boy in the 'two children' problem seems incorrect. The combinations for bb should account for the different outcomes based on the names of the boys, which may not have been fully considered.
For Puzzle #8, if both children are boys born on Tuesday, you should only count that day once, not twice.
The two children question has the answer wrong; it is 1 chance in two or 50%. The answer given is incorrect as it appears to ignore the fact that the second son can be born on any day of the week, therefore the day of the week is not a variable and the only factor that changes is whether it is a girl or a boy.
The two children question has the answer wrong. It is 1 chance in two or 50%, as the second son can be born on any day of the week. The answer given ignores this fact.
The Two Children solution contains a possibility that would mean both of them were boys born on a Tuesday, but we are told that one of them was born on a Tuesday. I got it wrong anyway.
Puzzle 8 on the Difficult Logic Puzzles page is incorrect. The question implies that one of them is a boy born on Tuesday, not at least one. This changes the probabilities significantly.
The probability of having two boys is still 1/2 since these are independent events. The solution provided is for the case where two boys are born on Tuesday, which is not specified in the problem.
Number 8 on difficult in the logical puzzles section is wrong. The probability you gave for having two boys where one is born on a Tuesday is correct, but that would be in a situation where either the boys weren't born or weren't known about yet.
The probability calculation for the two boys puzzle is incorrect; given one boy born on a Tuesday, the probability of the other child being a boy is 50%.
I previously mentioned that the probability for puzzle #8 is wrong; the calculation of 13/27 for having two boys with one born on Tuesday is incorrect.
The answer for 99 people saved doesn't make sense as it assumes the men in line know who is saved. The question states that any correct answer is unknown to all others. If the hats alternate colors, then everyone dies.
#8 (Two children) is balderdash. Given a mother has two children, and given one child is a boy, the probability the second child is a boy is in fact 1/2. The graph presented is misleading because it simultaneously considers two possible cases which should be considered independently.
I think that your "Two Children" problem is misleading. The parent confirms that one boy is born on a Tuesday, but it does not necessarily follow that the second child is not also a boy born on Tuesday.
I believe you forgot the upper-right hand quadrant of boys born on Tuesday, so the total should be 33 and the probability should be 13/33.
I think the probability will be 1/2 because the condition of asking if the child was born on Tuesday doesnโt make a difference. The child can be born any day, and it doesn't matter if they are younger or older.
I believe the probability of the second child being born on a Tuesday is 1/2. The condition of asking if he was born on Tuesday doesn't change the overall probability, as the child can be born any day.
I believe the puzzle regarding two children, one of which is a boy born on Tuesday, is incorrect. I believe the answer is 1/2, not 13/27. Using the chart, the tile in which the column and row intersect, where both are boys born on Tuesday, should be counted twice.
On the two children problem: Assuming the parents meant one or two boys born on Tuesday, we can conclude the following: The parents rolled a 14 equal-sided die twice and at least once rolled a 3.
In your difficult logic puzzles, question 8, you say that the answer is 13/27 possibility. However, I disagree with this. If we don't consider the day of birth, there is a 1/2 chance that a newborn child will be a boy.
I disagree with the answer of 13/27 for question 8. If we consider the possibility of having two boys without the day of birth, the chance would be 1/4. Knowing one child is a boy changes the calculation.
The question is incorrect; the state 'BB' has a multiplicity of 2 and thus gives a different probability.
You have ambiguity in the last question you need to eliminate: 'I ask people at random if they have two children and also if one is a boy born on a Tuesday.' What exactly does the phrase 'if one is a boy' mean?
The probability question regarding two children and one being a boy born on a Tuesday is intriguing. However, the relevance of the day of the week should be explained further.
The probability question about two children is interesting, but the specific details about the boy born on a Tuesday can be misleading. It would be helpful to clarify how this affects the overall probability.
The 'two children' answer is wrong. The boy referenced in the question is either the first or second child, and there's a 50% chance the second child is male in either case.
The answer to the 'two children' puzzle is incorrect. The boy referenced can only be either the first or second child, leading to a 50% chance for each. The graph's highlighted lines create an impossible instance where the boy is both the first and second child.
The wording of the Two Children puzzle should be changed to clarify that it refers to children born on Tuesday, not just one being a boy born on Tuesday.
The solution to the two children riddle is wrong. There's a possibility that both children are boys born on Tuesdays, which isn't accounted for in the solution. The real chance is 14/28 (one half) not 13/27.
For question #8 "Two Children," the answer should be 1/2, not 13/27. The chart leaves out the "2nd" possibility of a Tuesday/Tuesday birthday scenario, which would make the chances of BB to be 14/28.
Regarding the difficult "two children" puzzle, I was wondering if you could provide more detail as to the solution. The inclusion of a 7-day week seems arbitrary; if we had a 10-day week, the answer would be 19/39.
The answer to the Two Children puzzle is incorrect; it should be 1/2 as most people guess. The logic used to arrive at 13/27 is not convincing.
I think the answer for question #8 (Two Children) is incorrect. We already know that the first child is a boy. So the real question becomes: what is the probability that the second child is a boy? The probability of the second child being a boy is independent from the fact that the first child is a boy born on a Tuesday. Since the chance of giving birth to either sex is equal, the probability of the second child being a boy is 1/2 = 50%.
I believe the answer to question #8 (Two Children) is incorrect. The probability question regarding having two boys needs clarification.
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