To calculate the probabilities, we need to know the total number of balls in the bag. Since there are 6 red balls, 9 blue balls, and 5 green balls, the total number of balls in the bag is 6 + 9 + 5 = 20.
(a) To calculate the probability that both balls chosen are red with replacement, we can multiply the probability of choosing a red ball on the first draw (6 out of 20) with the probability of choosing a red ball on the second draw (also 6 out of 20), since the ball is replaced after each draw. Therefore, the probability is (6/20) * (6/20) = 36/400 = 9/100.
(b) To calculate the probability that one ball is blue and the other is green, we can multiply the probability of choosing a blue ball on the first draw (9 out of 20) with the probability of choosing a green ball on the second draw (5 out of 20). However, since the order of drawing blue and green doesn't matter, we need to account for both possibilities. So, the probability is (9/20) * (5/20) + (5/20) * (9/20) = 45/400 + 45/400 = 90/400 = 9/40.
(c) To calculate the probability that both balls are of the same color, we can add the probability of both balls being red (9/100) with the probability of both balls being blue or both balls being green. Since there are 9 blue balls and 5 green balls in the bag, the probability of both balls being blue or both balls being green can be calculated as (9/20) * (8/20) + (5/20) * (4/20) = 72/400 + 20/400 = 92/400 = 23/100.
So, the probabilities are:
(a) Both are red: 9/100
(b) One is blue, the other is green: 9/40
(c) They are of the same color: 23/100