A card is chosen from a deck of 52 cards. It is put back in the deck and a second card is chosen. What is the probability of an ace and a 2?
A) $\frac { 1 } { 13 }$
B) $\frac { 1 } { 8 }$
C) $\frac { 2 } { 169 }$
D) $\frac { 2 } { 13 }$
E) $\frac { 1 } { 169 }$

Question

Quizplus · Accepted Answer

The probability of drawing an ace and a 2 is the product of the probability of drawing an ace and the probability of drawing a 2, given that the first card drawn was not an ace.
The probability of drawing an ace on the first draw is $\frac{4}{52} = \frac{1}{13}$
The probability of drawing a 2 on the second draw, given that the first card drawn was not an ace, is $\frac{4}{51}$
Therefore, the probability of drawing an ace and a 2 is $\frac{1}{13}\cdot\frac{4}{51} = \frac{4}{663} = \boxed{\frac{1}{169}}$

A Card Is Chosen from a Deck of 52 Cards 113\frac { 1 } { 13 }131​

A Card Is Chosen from a Deck of 52 Cards $\frac { 1 } { 13 }$