Question

Family A and Family B each have 2 children. At least one of Family A’s children is a boy, and Family B’s oldest child is a boy.
a. Find the probability that Family A has 2 boys.
b. Find the probability that Family B has 2 boys

Answer 1

a. 0.5
b. 0.5

Answer 2

a: 1/3
b: 1/2

Answer 3

in case a, you don't know WHICH is a boy, though. So you have 4 possibilities for having 2 kids:
BB, BG, GB, GG
they say "at least one is a boy" which narrows the possibilities to:
BB, BG, GB
the probability that both are boys is 1/3

Answer 4

In b, the choices are:
BB, GB
and the probability is 1/2.

Answer 5

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

Answer 6

right. so it depends on how you find out at least one is a boy. if you are just told "at least one is a boy," the probability is 1/3.

Answer 7

Thank you all for your explanations! You're exactly right, and it makes a lot of sense. I really appreciate your help!

Answer 8

Can anyone help me figure out another question? For part a, I got 2/12 (or 1/6). For part b, I got 1/6. Not sure if I am right, though.

Answer 9

A box contains 4 tickets: red ticket #1, red ticket #2, green ticket #1 and green ticket #2. Two tickets are drawn from the box without replacement. (Consider doing some random sampling first.)
a. Find the probability that both tickets chosen are red given that at least one of them is red.

b. Find the probability that both tickets chosen are red given that at least one of them is red ticket #1.

Answer 10

For part b, I meant to say I got 1/12.

Answer 11

the probability of picking 2 reds is 1/4 * 1/3 = 1/12. But if you are given that you got "at least one red", that eliminates 2 of the possibilities: "G1, G2" and "G2, G1". So the chances are 1/10. if you are given that "at least one of them is R1" that eliminates the six possibilities "G2, G1", "G1, G2", "R2, G1", "R2, G2", "G1, R2", "G2, R2", for a probability of 1/2.

Answer 12

wait, I'm totally wrong.

Answer 13

it's 2/10 = 1/5 and 2/6 = 1/3.

because the probability of picking 2 reds is 1/2 * 1/3 = 2/12. then using the same logic, we have 2/10 because we are eliminating 2 choices with "at least one red" and 2/6 because we are eliminating 6 choices with "at least one is R1".

Answer 14

@hickninja: you are the master of probability! :-) Thank you so much for your explanations. I forgot to eliminate those choices. I'd give you another medal, but it won't let me do so in this window.