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
This really depends on how the questions is phrased precisely. But here is one way in which obtaining information changes the probability, or at least your belief in the evidence.
>A friend of yours invites you over. He says he has 2 children.
At this stage you are in one of four possible worlds: BB; BG; GB; GG
We will assume these have equal probability. So the probability of BB is 1/4.
>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.
We can now rule out the fourth world. We are either in BB; BG; or GB. We will also assume each child is equally likely to open the door. Therefore the probability of BB is 1/3.
It’s also worth pointing out that some interpretations of probability don’t allow claims about single events (e.g. [frequentist interpretation](https://en.wikipedia.org/wiki/Probability_interpretations)).
As an aside – are you saying your bachelor’s degree in biology had no statistics? How is that even possible?
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