Mystic Margo is a magician. She enlists the help of an audience member, Adam. Adam and the rest of the audience are shown a random number N from 1 to 10, but Margo can’t see what the number is. Out of Margo’s sight, Adam is given a pack of cards numbered from 1 to N, and asked to shuffle them and then select just one card at random to show Margo. Let X be the number on the card that Adam shows to Margo.

Suppose Adam shows Margo the card X = 5. Find the probability distribution P(N = n | X = 5). You may assume that the original number N was drawn from the distribution with P(N = n) =

1 10 for n = 1, . . . , 10.

If Margo’s aim is to guess the value of N, what value should she guess?