Tagged: probability

Two moms, Sarah and Courtney, are talking to each other.
Sarah: I have two children.
What is the probability that both of Sarah’s children are boys?Courtney: Me too! Do you have any boys?
What is the probability that both of Courtney’s children are boys?Sarah: Yes, I do! What is your younger child?
What is the probability that both of Sarah’s children are boys?Courtney: It is a boy. He is so mischievous!
What is the probability that both of Courtney’s children are boys?Sarah: Is he Sagittarius? Sagittarius boys are known to drive their mothers crazy. I can also testify from personal experience.
What is the probability that both of Sarah’s children are boys?Courtney: No, but actually I have the opposite personal experience to yours.
What is the probability that both of Courtney’s children are boys?Sarah: Well, I guess astrology does not always get it right.
Courtney: Well, I guess it does about half of the time.
Puzzle from the archives.

The solution is provided HERE. Some notes regarding this puzzle…
This puzzle is a variation of the classic “Boy or Girl” paradox. The confusing part is that if you know that at least one of the siblings is a boy, then the chance that both siblings are boys is 1/3 instead of 1/2. To see that indeed this is the case, note that these 3 outcomes for the older and the younger child (in this order) are equally possible:
 BOY BOY – 1/3
 BOY GIRL – 1/3
 GIRL BOY – 1/3
Therefore, the probability that the outcome is 1., is equal to 1/3.
An even more confusing question is: “If you know that (at least) one of the siblings is a boy born in January, what is the chance that both siblings are boys?”. While it looks like the month of birth is irrelevant to the question, it actually alters the probability. This can be again easily seen by writing all possible outcomes:
 BOY (January) BOY (January) – 1/47
 BOY (January) BOY (Not January) – 11/47
 BOY (Not January) BOY (January) – 11/47
 BOY (January) GIRL – 12/47
 GIRL BOY (January) – 12/47
Therefore, the probability that the outcome is 1., 2., or 3., is equal to 23/47.
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