You pick a card at random. Without putting the first card back, you pick a second card at random.1234What is the probability of picking a 1 and then picking a factor of 24?Write your answer as a decimal.

The problem involves two independent events: picking a 1 and then picking a factor of 24.

Step 1: Determine the total number of outcomes. Assuming we are picking from a standard deck of 52 cards, there are 52 possible outcomes for the first pick and 51 for the second (since we are not replacing the first card).

Step 2: Determine the favorable outcomes for the first event. The number 1 corresponds to an Ace in a deck of cards. There are 4 Aces in a deck, so the probability of picking an Ace (or a 1) is 4/52 = 0.0769.

Step 3: Determine the favorable outcomes for the second event. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. In a deck of cards, these correspond to Aces, 2s, 3s, 4s, 6s, 8s, Queens (12), and no card (24). Since we have already picked one card, there are now 3 Aces, 4 2s, 4 3s, 4 4s, 4 6s, 4 8s, and 4 Queens left. So, there are 3 + 4*7 = 31 favorable outcomes. The probability of picking a factor of 24 is 31/51 = 0.6078.

Step 4: Multiply the probabilities of the two events. The probability of both events occurring is the product of their individual probabilities: 0.0769 * 0.6078 = 0.0467.

So, the probability of picking a 1 and then picking a factor of 24 is approximately 0.0467, or 4.67% when expressed as a percentage.