Question

Poker is a card played with a standard 52 card playing deck. We draw one card at a time without replacement from the top of a shuffled standard poker deck and stop when we draw an ace. Let X be the number of cards we have drawn. What is P( X = 5 ) ? Round to two decim

Answer 1

Answer:

0.0599

Step-by-step explanation:

There are four aces in a standard 52-card deck. If X=5, the first ace must be drawn exactly at the fifth pick, which means that the probability of X=5 is the probability of not getting an ace in the first four picks and getting an ace in the fifth pick:

$P(X=5)=\frac{48}{52}* \frac{47}{51}* \frac{46}{50}* \frac{45}{49}*\frac{4}{48}\\ P(X=5) =0.0599$

The probability that X=5 is 0.0599