Suppose you choose a marble from a bag containing 3 red marbles, 5 white marbles, and a blue marbles. You return the frat marble to the bag and then choose again. Find P (red and blue).

Answer 1

To find the probability of choosing a red marble first and then a blue marble from the bag, we'll follow these steps:

1. **Determine the total number of marbles in the bag.**
- There are 3 red marbles, 5 white marbles, and 1 blue marble.
- Total number of marbles = 3 (red) + 5 (white) + 1 (blue) = 9 marbles.

2. **Calculate the probability of choosing a red marble first.**
- Probability of choosing a red marble = Number of red marbles / Total number of marbles = 3 / 9 = 1 / 3.

3. **Since the marble is returned to the bag, the total number of marbles remains the same (9) for the second draw.**

4. **Calculate the probability of choosing a blue marble on the second draw.**
- Probability of choosing a blue marble = Number of blue marbles / Total number of marbles = 1 / 9.

5. **Now, multiply the probabilities of the individual events to get the combined probability of both events happening in sequence:**
- P(red and blue) = P(red first) × P(blue second)
- P(red and blue) = (1 / 3) × (1 / 9) = 1 / 27.

So, the probability of drawing a red marble first and then a blue marble after replacing the first marble is \( \frac{1}{27} \).