Question

Cards are dealt by drawing uniformly at random from a deck of cards without replacement until the first ace appears. What is the chance that at most 3 deals are required given that at most 6 deals were required?

Answer 1

Answer:

Given that:

Cards are dealt by drawing uniformly at random from a deck of cards without replacement until the first ace appears.

1) The required probability is

P(3|6) using Baye's theorem it is

where

P(3) is the probability that at most 3 deals are required and P(6) is the probability that at most 6 deals are required.

P(3) is actually the complement of the event where ace doesn't appear in first 3 deals. So

Similarly for P(6)

So,