Question

This bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. Marbles are drawn twice, with replacement. Find the probability of each compound event. Drawing a red marble, then a green marble.

a) 3/20
b) 1/30
c) 1/20
d) 1/15

Answer 1

The probability of drawing a red and then a green marble, with replacement, is the product of the individual probabilities which is (3/10)*(2/10) = 3/50. However, this correct probability is not among the provided options.

Step-by-step explanation:

The student asked about finding the probability of drawing a red marble followed by a green marble when marbles are drawn twice with replacement from a bag containing 3 red marbles, 5 blue marbles, and 2 green marbles. To calculate this compound probability, we multiply the probability of each independent event.

First, find the probability of drawing a red marble. Since there are 3 red marbles out of a total of 10 (3 red + 5 blue + 2 green), the probability is 3/10.

Since the first marble is replaced, the probabilities for the second draw remain the same. Therefore, the probability of drawing a green marble on the second draw is 2/10, as there are 2 green marbles out of the 10 total.

To find the probability of both events happening in sequence, multiply the two probabilities: (3/10) * (2/10) = 6/100 = 3/50. Unfortunately, this correct result is not listed in the provided options.