Bayes theorem and conditional probability example.

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Greetings to all.
I started an MSc that includes a course in statistics. Full disclosure: my bachelor’s had no courses of statics and it is in biology.

So, the professor was trying to explain the Bayes theorem and conditional probability through the following example.
“A friend of yours invites you over. He says he has 2 children. When you go over, a child opens the door for you and it is a boy. What is the probability that the other child is a boy as well.”

The math say the probability the other child is a boy is increased the moment we learn that one of the kids is a boy. Which i cannot wrap my head around, assuming that each birth is a separate event (the fact that a boy was born does not affect the result of the other birth), and the result of each birth can be a boy or a girl with 50/50 chance.
I get that “math says so” but… Could someone please explain? thank you

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24 Answers

Anonymous 0 Comments

Edit: this is wrong, the chances the other kid is a boy is 50%.

Imagine there are 100 families with 2 kids.

25 have BB
25 have BG
25 have GB
25 have GG

So you have a 25% chance of visiting a family with 2 boys.

Now imagine you know the family has 1 boy.

Your possible families are

25 with BB
25 with BG
25 with GB

So before it was 25/100 (1/4) chance of happening to visit a BB family but now it’s 25/75 (1/3)

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