Probability

In a standard deck of 52 cards, there are 4 aces. Therefore, the probability of drawing an ace on a single trial is given by:
‌ Probability ‌=‌

4

52

=‌

1

13

When drawing two cards with replacement, the situation can be modeled using a binomial distribution where the number of trials is 2 and the probability of success (drawing an ace) is ‌

1

13

.
The mean (or expected value) of a binomial distribution is calculated as:
Mean = Number of trials × Probability of success =2×‌

1

13

=‌

2

13

Therefore, the mean of the probability distribution of X, where X denotes the number of aces drawn, is ‌

2

13

.