A bag contains 4 white, 3 blue, and 5 red marbles.
Find the probability of choosing 3 blue marbles in a row if the marbles are replaced.
A. two over eleven
B. one over two hundred twenty
C. Fraction 1 over 27 end fraction
D. one over sixty-four.
The probability of choosing one blue marble on any given draw is 3/12 or 1/4. Since the marbles are replaced each time, the probability of choosing three blue marbles in a row is (1/4)^3 or 1/64. Therefore, the answer is D. one over sixty-four.
To find the probability of choosing 3 blue marbles in a row with replacement, we need to determine the probability of choosing a blue marble on each individual draw.
There are a total of 12 marbles in the bag, and 3 of them are blue. So, the probability of choosing a blue marble on the first draw is 3/12.
Since we are replacing each marble after drawing, the probability of choosing a blue marble on the second draw is also 3/12.
Similarly, the probability of choosing a blue marble on the third draw is 3/12.
To find the overall probability, we multiply the probabilities of each individual draw:
(3/12) * (3/12) * (3/12) = 27/1728 = 1/64
Therefore, the correct answer is D. One over sixty-four.