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
Initially the odds that both kids are boys is 1 in 4. However if you know one of the kids is a boy then the odds the other kid is a boy is 1 in 2. The chance that both kids are boys goes up if we know that one of the kids is a boy.
It’s a poorly worded question for sure, but anyone saying the odds of both being boys only goes to 1 in 3 should read R2Dude2’s comment https://old.reddit.com/r/explainlikeimfive/comments/y8ucgq/eli5_bayes_theorem_and_conditional_probability/it2vxnx/ because you’re missing the probability that either kid answers the door. Not only does seeing a boy mean it’s not the girl girl scenario, but it’s also not the boy-girl scenarios where a girl answers the door which halves the boy girl scenarios as well.
Edit to clarify:
Of 4 houses 1 house has 2 boys (BB), 2 have 1 boy 1 girl (BG), and 1 has 2 girls (GG). The kid who answers the door is random (50-50). Since a boy answers the door you have to eliminate the GG house AND one of the BG houses where the girl answered the door (50-50), leaving 1 BG house (where the boy answers the door) and 1 BB house.
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