Final answer:
The probability of picking out a red marble, placing it in his pocket, and then picking out a second red marble is 28/95.
Step-by-step explanation:
The probability of picking out a red marble, placing it in his pocket, and then picking out a second red marble can be calculated as follows:
First, we need to find the probability of picking a red marble on the first draw. There are a total of 20 marbles in the bag (9 blue + 8 red + 3 white), and 8 of them are red. Therefore, the probability of picking a red marble on the first draw is 8/20.
After placing the first red marble in his pocket, there are now 19 marbles left in the bag. Out of these 19 marbles, 7 are red. Therefore, the probability of picking a second red marble is 7/19.
To find the probability of both of these events happening, we multiply the individual probabilities: (8/20) * (7/19) = 28/95.