Suppose you have a standard deck of 52 cards and are drawing

Suppose you have a standard deck of 52 cards and are drawing them with- out replacement. Determine the chance of the following (you will have to symbolize them first):

(a) Drawing an ace on the first draw.

(b) Drawing two aces in two draws.

(c) Drawing at least one ace in the first two draws.
(d) Drawing a spade given that you have already drawn 4 spades.

Solution

(a) Drawing an ace on the first draw. 4/52=1/13 (b) Drawing two aces in two draws. 4/52*3/51=3/663 (c) Drawing at least one ace in the first two draws. 1-48/52*47/51=1-564/663=99/663 (d) Drawing a spade given that you have already drawn 4 spades 9/48