Question

Suppose that an ordinary deck of 52 cards is shuffled and the cards are then turned over one at a time until the first ace appears. Given that the first ace is the 20th card to appear, what is the conditional probability that the card following it is the
(a) ace of spades?
(b) two of clubs?

Answer 1

Answer:

Step-by-step explanation:

Given that an ordinary deck of 52 cards is shuffled and the cards are then turned over one at a time until the first ace appears.

the first ace is the 20th card to appear

This implies that there are still 32 cards with 3 aces in it.

But 2 clubs can be either 1 remaining or nothing remaining

a) ace of spades

3 aces out of 32

Prob = $\frac{3}{32}$

b) 2 of clubs

P (2 club already gone in first 19 cards) +P(2 club is in the remaining)

= 0+P(first 20 cards not 2 clubs )*P(2 club in 21st draw)

= $(\frac{51}{52} )(\frac{1}{32}) \\\\= \frac{51}{1664}$