Bag with 100 coins. One of them is double headed, the rest are fair. You flip it n times and get n heads. What would your intuition be on whether you have the double headed coin or not? What would the probability be that you have the double headed coin be as n goes to infinity? How many flips would it take for you to be 50% sure? You flip it seven times, what is the probability you have the double headed coin?

X and Y are two independent variables with uniform distributions form 0 to 1. Z = X + Y. What is the variance of Z. What is the correlation between X and Z? What does the distribution of Z look like?

A coding question. You have a list of integers, how do you write a code to find the largest integer in the list and the number of times it appears?