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 black card, and the third card will be the five of clubs. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

`(1)/(416)`

Step-by-step explanation

To find the probability that the first card will be a spade, the second card will be a black card, and the third card will be the five of clubs, we have to find the products of the probabilities of each of the events.

There are 52 cards in a standard deck of cards. Since the cards are drawn with replacement, it means that for each event, there are 52 cards.

There are 13 spades in a standard deck of cards. Hence, the probability that the first card will be a spade is:

`P(spade)=(13)/(52)=(1)/(4)`

There are 26 black cards in a standard deck of cards. Hence, the probability that the second card will be a black card is:

`P(black\text{ }card)=(26)/(52)=(1)/(2)`

There is only one five of clubs in a deck of cards. Hence, the probability that the third card will be a five of clubs is:

`P(five\text{ }of\text{ }clubs)=(1)/(52)`

Therefore, the probability that the first card will be a spade, the second card will be a black card, and the third card will be the five of clubs is:

`\begin{gathered} P=(1)/(4)*(1)/(2)*(1)/(52) \\ P=(1)/(416) \end{gathered}`

That is the answer as a fraction in the lowest terms.