Question

You pick a card at random, put it back, and then pick another card at random. What is the probability of picking a 3 and then picking a divisor of 6?

1) 1/6
2) 1/3
3) 1/2
4) 2/3

Answer 1

The probability of picking a 3 and then picking a divisor of 6 is 1/169.

Step-by-step explanation:

To find the probability of picking a 3 and then picking a divisor of 6, we need to consider the outcomes for each step.

Step 1: Picking a 3. There are 4 cards with a value of 3 in a standard deck of 52 cards, so the probability is 4/52.

Step 2: Picking a divisor of 6. There are 4 divisors of 6: 1, 2, 3, and 6. Since we put the first card back, all 52 cards are available for the second pick, so the probability is 4/52.

To find the overall probability, multiply the probabilities of each step. Therefore, the probability of picking a 3 and then picking a divisor of 6 is (4/52) * (4/52) = 16/2704, which simplifies to 1/169.

So, the correct answer is option 1) 1/6.