Question

Two cards are chosen from those shown below, without replacement (13 cards are shown). What is the probability that both cards are multiples of 3? Express your answer as a decimal and round to the nearest thousandths.

Answer 1

To find the probability of choosing two cards that are multiples of 3, determine the number of favorable outcomes and the total number of possible outcomes. Then, divide the number of favorable outcomes by the total number of possible outcomes. In this case, there are 4 multiples of 3 out of 13 cards, and the probability is approximately 0.615.

Step-by-step explanation:

To find the probability that both cards are multiples of 3, we need to determine the number of favorable outcomes and the total number of possible outcomes.

There are 13 cards shown, and of those, there are 4 multiples of 3: 3, 6, 9, 12. When we choose the first card, there are 13 options, and for the second card, there are 12 options remaining. Therefore, the number of favorable outcomes is 4 * (13 * 12) = 624.

The total number of possible outcomes is the number of ways to choose 2 cards from the 13 shown, which can be calculated using the combination formula: C(13,2) = 13! / (2! * (13-2)!) = 78.

So, the probability that both cards are multiples of 3 is 624 / 78 = 8 / 13, which rounds to approximately 0.615.