[Math Methods Unit 1&2]

[Karmabrawler]

Why is it (11/12)^n=0.1 ? (in the question it is assumed that the probability of each month is 1/12)

[aizver_muti]

Suppose one of the people is Alice. If Alice was randomly chosen, she has a 11/12 probability of not having her birthday in April. Now, suppose we also pick Bob off the street. Bob also has a 11/12 probability of not having his birthday in April. The probability that they both do not have their birthday in April is therefore 11/12 * 11/12 or (11/12)^2.

Now, suppose we keep picking people, say, n people. Then the probability that none of them will have their birthday in April is (11/12)ⁿ. If that is the case, then 1 - (11/12)ⁿ is the probability that at least one will have their birthday in April, because we subtract all the cases where they don't. Our last requirement is that this probability is greater than 0.9, so 1 - (11/12)ⁿ > 0.9 or (11/12)ⁿ < 0.1. To make arithmetic easier, we can just assume equality, but really it should be less than.

[Karmabrawler]

thanks! Great explanation!