January 4, 200818 yr Here's one that has brought about a lot of discussion from students and puzzle fans alike over the years. I have had many people question me about this one. Even after I espouse my credentials of teaching probability and statistics for twenty years, some still question this one. It is really not a particularly difficult puzzle, but it is one that ,once you have the answer, it may not "feel" quite right. Some of you will probably get it right away; some will say I am wrong. Here goes: ******************************************************* Mrs. Mathemagician has three children, at least one of which , is a boy. What is the probability that she has three sons? *******************************************************
January 4, 200818 yr I was torn between 1 in 3 and 1 in 4. It looks like there are 3 possible choices, 2 boys and a girl, 1 boy and 2 girls, and 3 girls, but they don't have equal chances of occuring. But in reality there are 4 possiblities: BBB, BGG, BBG and BGB. So the odds of having two boys and one girl are 50/50 and the odds of having all boys or two girls are each 1 in 4.
January 4, 200818 yr Author I'll make it multi-choice. Pick a letter: (a) 1/3 (b) 1/4 © 1/6 (d) 1/7 (e) 1/8
January 4, 200818 yr We are assuming that each pregnancy has a 50/50 chance, which we are finding out is not necessarily true. Some couples are more prone to having children on the same sex....ask my neighbor with 5 girls. If we are talking strictly math here, I would say, there are three possible scenarios. One boy and 2 girls Two boys and 1 girl Three boys So I would say 1 in 3.
January 4, 200818 yr (d) 1/7 There are 8 potential combos when having three kids: BBB BBG BGB BGG GGG GGB GBG GBB Since it said "...at least one is a boy", that rules out the GGG, leaving 7 different choices. (Remember, it does not say that the first child is a boy.) Only one of the choices is all three boys. Hence, one in seven chance.
January 4, 200818 yr I know a lady that had 9 children, all of which were boys. You have a 50/50 shot at having a boy everytime.
January 4, 200818 yr My guess is 1 in 3. You know one is a boy so no reason to factor him in. The remaining 2 childern can either be BB, BG, GG. So my answer is A.
January 4, 200818 yr I'll make it multi-choice. Pick a letter: (a) 1/3 (b) 1/4 © 1/6 (d) 1/7 (e) 1/8 (D) 1/7
January 4, 200818 yr 1/4 (1/2 times 1/2; since one is already a boy - if that hadn't already been stated, the answer would be 1/8).
January 4, 200818 yr My guess is 1 in 3. You know one is a boy so no reason to factor him in. The remaining 2 childern can either be BB, BG, GG. So my answer is A. That answer would be correct, except you left out the fourth possibility - GB.
January 4, 200818 yr A variation of this question used to come up in elementary statistics class. Mrs. A has three boys. What is the probability that her next child will be a boy? Of course, the answer is 1/2, but there were an AWFUL lot of folks who read more into it than necessary.
Archived
This topic is now archived and is closed to further replies.