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
Think of it another way:
The professor tells you that you will be visited by four people. Each one will either give you a dollar or give you nothing. What are the chances of getting at least $2 in the end? Basically, you need two of the four people to give you a dollar.
Now, the first one visits you and gives you a dollar. What are the chances now that you will have at least $2 in the end? You only need one of the next three to give you a dollar. The chances of getting to $2 are higher than before, because you’re halfway there.
Each visitor’s decision is independent, but your chances of having $2 in the end is conditioned by how much you have in your hand at each point. You can’t predict the choice the visitor will make, but the number of possible outcomes changes – i.e. you can’t end up with no dollars once you already have $1.
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