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
In: 77
It seems that your main confusion is why information about one child gives information on the other.
The important thing to note it that you’re not given information about one child in particular. You’re given information about BOTH children as a whole: at least one of them is a boy. That’s why it gives you additional information about the the combined identity of BOTH children.
If the question was instead “Given that the YOUNGER child is a boy…” Then you don’t have any additional information about the elder one, they still have 50/50 of being boy or girl.
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