in a deck of 52 cards, what is the probability of randomly selecting an ace, replacing it, and then…

Explanation:

Step1: Calculate probability of selecting an ace

There are 4 aces in a 52 - card deck. The probability of selecting an ace, $P(A)$, is $\frac{4}{52}=\frac{1}{13}$.

Step2: Calculate probability of selecting a king

There are 4 kings in a 52 - card deck. Since the first card is replaced, the probability of selecting a king, $P(K)$, is $\frac{4}{52}=\frac{1}{13}$.

Step3: Calculate the joint - probability

Since the two events are independent (because of replacement), the probability of both events occurring is the product of their individual probabilities. So $P(A\cap K)=P(A)\times P(K)$. $P(A\cap K)=\frac{1}{13}\times\frac{1}{13}=\frac{1}{169}$

Answer:

$\frac{1}{169}$