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)?

Answer 1

Explanation:

Given that 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.

There are 4 aces and 48 non aces.

For randomly drawing card for first card we have probability for drawing ace = 4/52 and non ace = 48/52

X = no of cards we have drawn

If X is the total no of cards drawn, then the event should have been

first x-1 cards non aces, and the last card ace.

Hence P(X)

= Drawing x-1 cards from 48 non aces * drawing one card from remaining 52-(x-1) cards

=
`(48C(x-1))/(52C(x-1)) *(4)/(53-x) \\`, x=1,2,.....49