2.

Question

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 \(\frac{1}{12}\).