Five cards are drawn from a standard deck of cards. each card is replaced after being drawn. what is the probability of the following event: p(3 and 3 and 3 and 2 and 2)?

General Idea:

If A and B are independent, then the probability that events A and B both occur is:

In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B

Applying the concept:

Five cards are drawn from a standard deck of cards. Each card is replaced after being drawn.

There are four 3's in a deck of card, four 2's in a deck of card. In a deck of card there are 52, so...

\; =\; p(3) \times \; p(3) \times \; p(3) \times \; p(2) \times p(2) " alt=" p(3\; and\; 3\; and\; 3 \; and \; 2 \; and\; 2)=\frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \\ \\ Multiply \; numerator \; with \; numerator \; and \; denominator \; with \; denominator\\ \\ \frac{4 \cdot 4 \cdot 4 \cdot 4 \cdot 4}{52 \cdot 52 \cdot 52 \cdot 52 \cdot 52} \\ \\ Cancel \; Common\; Factor\\ \\ \frac{1 \cdot 1 \cdot 1 \cdot 1 \cdot 1}{13 \cdot 13 \cdot 13 \cdot 13 \cdot 13} =\frac{1}{13^5} =\frac{1}{371293}" /> \; =\; p(3) \times \; p(3) \times \; p(3) \times \; p(2) \times p(2) " />

a is the correct