Question

3 multiple choice 4 points if two cards are drawn from a standard deck of 52 cards without replacement, what is the probability that both cards are fives? 1/4 1/3 2/52 4/52 3/51 5/52 * 4/51

Explanation:

Step1: Calculate first - card probability

There are 4 fives in a 52 - card deck. The probability of drawing a five as the first card is $\frac{4}{52}$.

Step2: Calculate second - card probability

Since we do not replace the first card, there are now 51 cards left in the deck and 3 fives left. So the probability of drawing a five as the second card, given that the first card was a five, is $\frac{3}{51}$.

Step3: Calculate joint probability

By the multiplication rule for dependent events, the probability that both cards are fives is the product of the probabilities of each event, which is $\frac{4}{52}\times\frac{3}{51}$.

Answer:

$\frac{4}{52}\cdot\frac{3}{51}$ (corresponding to the third option in the multiple - choice)