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
Before you went there, if someone asked you to guess the genders of the two kids, you’d naturally think, it could be anything: any one of BB, BG, GB, GG. You have one in four chances of being right.
But when a boy opens the door, you can certainly eliminate GG as a possibility. But it could still be one of the other choices, so you have one in three chances of being right. What has happened is that you have gained information, and based on that information (“conditional to that information”), your guesswork has improved (“higher probability”). More information equates to less uncertainty, which improves the odds you place on that event.
Remember that the theory of probability has long been associated with gambling and insurance, which is tied to how much money you are willing to wager on something. The higher the probability, the less risky a wager it becomes.
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