23.Suppose you choose a marble from a bag containing 6 red marbles, 3 white marbles, and 4 blue marbles. You return the first marble to the bag and then choose again. Find P(red and blue).

a. 10/13
b. 9/13
c. 24/169
d. 24/13

P(R)=6/13

P(B)=4/13
Since the marble is returned to the bag, the first and the second picks are independent events, and probability of both happening is the product of the two probabilities.

To find the probability of selecting a red and blue marble, we need to find the individual probabilities of selecting a red marble and then a blue marble.

Step 1: Finding the probability of selecting a red marble.
There are a total of 6 red marbles out of the 6 red, 3 white, and 4 blue marbles in the bag. Therefore, the probability of selecting a red marble on the first draw is 6/13.

Step 2: Returning the first marble to the bag.
After selecting the first marble, it is returned back to the bag. This means that the number of red marbles remains the same, i.e. 6.

Step 3: Finding the probability of selecting a blue marble.
Now, there are a total of 4 blue marbles out of the 6 red, 3 white, and 4 blue marbles in the bag. Therefore, the probability of selecting a blue marble on the second draw is 4/13.

Step 4: Finding the probability of both events happening.
To find the probability of two independent events occurring, we multiply their individual probabilities. In this case, the probability of selecting a red marble and then a blue marble is (6/13) * (4/13) = 24/169.

So, the answer is c. 24/169.