Question

you draw one card from a 52 - card deck. then the card is replaced in the deck and the deck is shuffled, and you draw again. find the probability of drawing an ace each time. click the icon to view a description of a standard deck of playing cards. the probability of drawing an ace each time is . (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate probability of drawing an ace first - time

There are 4 aces in a 52 - card deck. So the probability of drawing an ace in the first draw is $\frac{4}{52}=\frac{1}{13}$.

Step2: Calculate probability of drawing an ace second - time

Since the card is replaced and the deck is shuffled, the probability of drawing an ace in the second draw is also $\frac{4}{52}=\frac{1}{13}$.

Step3: Calculate the probability of both events

The two draws are independent events. For independent events $A$ and $B$, the probability of both $A$ and $B$ occurring is $P(A)\times P(B)$. So the probability of drawing an ace each time is $\frac{1}{13}\times\frac{1}{13}=\frac{1}{169}$.

Answer:

$\frac{1}{169}$