Question

You play a game where you first choose a positive integer n and then flip a fair coin n times. You win a prize if you get exactly 2 heads. How should you choose n to maximize your chance of winning?

Answer 1

n=2

Explanation:

In this question we are aiming at getting exactly two heads and trying to maximize our chances. Note that we must get two heads to get the prize and not anything different from that. Even if we get 1,3 or greater than three heads we wont get the prize as the condition specifies exactly 2 heads.

The number of results we get depends on the integer we choose. we need two results (2 heads) which can only be achieved by choosing n=2 as our positive integer.

Therefore to maximize our chances n=2