A card is chosen at random from a deck of 52 cards and then replaced. This is done a total of three times. What is the probability of getting a black card, the 4 of spades, and the jack of hearts?
A) $\frac { 1 } { 5,929 }$
B) $\frac { 1 } { 5,085 }$
C) $\frac { 1 } { 5,408 }$
D) $\frac { 1 } { 5,189 }$
E) $\frac { 1 } { 5,531 }$

Question

A card is chosen at random from a deck of 52 cards and then replaced. This is done a total of three times. What is the probability of getting a black card, the 4 of spades, and the jack of hearts?
A) $\frac { 1 } { 5,929 }$
B) $\frac { 1 } { 5,085 }$
C) $\frac { 1 } { 5,408 }$
D) $\frac { 1 } { 5,189 }$
E) $\frac { 1 } { 5,531 }$

Quizplus · Accepted Answer

The probability of getting a black card is $\frac{1}{2}$. The probability of getting a 4 of spades is $\frac{1}{52}$. The probability of getting a jack of hearts is $\frac{1}{52}$. Therefore, the probability of getting all three is $\frac{1}{2\cdot 52\cdot 52}=\frac{1}{5,408}$.

A Card Is Chosen at Random from a Deck of 52