Question

A bag contains 3 red marbles, 5 blue marbles and 2 green marbles. two marbles are drawn, one at a time from the bag. find the probability that both are blue under each condition. report answers to 3 decimal places.

a. after drawing out the first marble, it is replaced in the bag before drawing the second marble.

Answer 1

The probability of drawing two blue marbles, one at a time from a bag with replacement, is 0.25.

Step-by-step explanation:

The probability of drawing two blue marbles, one at a time from the bag with replacement, can be determined by calculating the probability of drawing a blue marble on the first draw and then multiplying it by the probability of drawing a blue marble on the second draw.

There are a total of 10 marbles in the bag (3 red + 5 blue + 2 green). The probability of drawing a blue marble on the first draw is 5/10 = 0.5. After the first blue marble is replaced, there are still 10 marbles in the bag, with 5 of them being blue. Therefore, the probability of drawing a blue marble on the second draw is also 5/10 = 0.5.

To find the probability of both marbles being blue, multiply the probabilities of each draw: 0.5 * 0.5 = 0.25.