You pick a card at random, put it back, and then pick another card at random.456What is the probability of picking a number less than 6 and then picking a factor of 8?Write your answer as a decimal rounded to the nearest thousandth.

To solve this problem, we need to consider two separate events: picking a card with a number less than 6 and picking a card that is a factor of 8.

1. Picking a card with a number less than 6: Assuming we are dealing with a standard deck of 52 cards (4 suits of 13 cards: Ace through 10, and the face cards Jack, Queen, King), the cards with numbers less than 6 are 1 (Ace), 2, 3, 4, and 5. Each of these numbers appears in 4 suits, so there are 4*5 = 20 such cards. The probability of drawing one of these cards is therefore 20/52 = 0.385 (rounded to the nearest thousandth).

2. Picking a card that is a factor of 8: The factors of 8 are 1, 2, and 4. Each of these numbers appears in 4 suits, so there are 4*3 = 12 such cards. The probability of drawing one of these cards is therefore 12/52 = 0.231 (rounded to the nearest thousandth).

Since we are replacing the card after the first draw, these two events are independent. The probability of both events occurring is the product of their individual probabilities: 0.385 * 0.231 = 0.089 (rounded to the nearest thousandth).

So, the probability of picking a card with a number less than 6 and then picking a card that is a factor of 8 is 0.089.