Question

2.
Suppose you choose a marble from a bag containing 3 red marbles, 5 white marbles, and 4 blue marbles. You return the first marble to the bag and then choose again. Find P (red and blue).

Answer 1

To find the probability of selecting a red marble and then a blue marble (in that specific order) from the bag, we follow these steps:

1. **Determine the total number of marbles in the bag**:
- Red marbles: 3
- White marbles: 5
- Blue marbles: 4
- Total marbles = \(3 + 5 + 4 = 12\)

2. **Calculate the probability of selecting a red marble on the first draw**:
\[
P(\text{Red}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{3}{12} = \frac{1}{4}
\]

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

4. **Calculate the probability of selecting a blue marble on the second draw**:
\[
P(\text{Blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{4}{12} = \frac{1}{3}
\]

5. **Now, find the joint probability of both events happening (selecting a red marble first and then a blue marble)**:
\[
P(\text{Red and Blue}) = P(\text{Red}) \times P(\text{Blue}) = \frac{1}{4} \times \frac{1}{3} = \frac{1}{12}
\]

Thus, the probability of selecting a red marble followed by a blue marble is \(\frac{1}{12}\).