1 a Take a wellshuffled deck of 52 playing cards and start o

1. (a) Take a well-shuffled deck of 52 playing cards and start opening cards one by one from the top. How long is the expected wait till the first ace?

(b) Now instead of opening cards from the top, draw a card randomly, and if not an ace, put it back in the deck. What is the probability that you will use at least 10 draws before seeing an ace?

1. (a) Take a well-shuffled deck of 52 playing cards and start opening cards one by one from the top. How long is the expected wait till the first ace? (b) Now instead of opening cards from the top, draw a card randomly, and if not an ace, put it back in the deck. What is the probability that you will use at least 10 draws before seeing an ace?

Solution

A.) 13 cards is the expected wait

52 / 4 aces = 13

B.) 48.6565%

52 - 4 aces = 48 non aces

(48/52) ^ 9 = 0.486565 chance of seeing no aces for 9 draws (at least 10 draws)