Question: Use any method you like to numerically compute the birthday probabilities: in a group of size n, the probability that at least two people have

  1. Use any method you like to numerically compute the birthday probabilities: in a group of size n, the probability that at least two people have the same birthday is Pn = 1 365! / (365 n)! 365n. Show that n = 23 is the first time Pn > 50%. What is the smallest value of n for which Pn > 90%?
  2. Two six-sided dice are rolled simultaneously.

(a) What is the probability that the numbers on top add to 6?

(b) What is the probability that at least one of the numbers is a 3?

(c) Given that one of the dice landed on 3, what is the probability the numbers add to 6?

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