Question

Three cards are drawn with replacement from a standard deck of 52 cards. Find the the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

Probability is expressed as

number of favorable outcomes/number of total outcomes

In a standard deck of cards, the total number of cards is 52.

There are 13 spades in a standard deck. Thus,

probability of selecting a spade = 13/52 = 1/4

There are 26 red cards in a standard deck of cards. Since the first card was replaced, the total number of cards remains 52.

probability of selecting a red card = 26/52 = 1/2

There are 4 queens in a standard deck of cards. Since the second card was also replaced, total number of cards is still 52. Thus,

Probability of selecting a queen = 4/52 = 1/13

Thus, the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen is

1/4 x 1/2 x 1/13

= 1/104