A deck of 52 cards is shuffled. What is the expected number of cards you need to draw to see the first ace?

A deck of 52 cards is shuffled. What is the expected number of cards you need to draw to see the first ace?

Approach: Use linearity of expectation or symmetry argument.

Consider the positions of the 4 aces and 48 non-aces. The expected position of the first ace is (52+1)/(4+1) = 53/5 = 10.6.

Follow-up: What is the expected number to see all 4 aces?

Key concepts: linearity of expectation, symmetry.