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
> What is the probability that the other child is a boy as well.
The problem is that the phrasing question is mis leading. In a certain sense, you can still answer that with 0.5 because of independence as you mentioned before.
The actual question is:
* Given the 1st kid is a boy, what is the probability that it is a BB situation?
Before we answer that question, let me ask another simpler question:
* What is the probability that it is a GG situation (without knowing anything else)?
Obviously the answer is 1/4
* What is the probability that it is a GG situation GIVEN that the 1st kid is a boy?
I hope it is obvious why here, the answer is zero, not 0.5 . It cannot ever be a GG situation because we already know that the 1st kid is a boy.
It is in this context why the P(BB|BX) is not 1/2.
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