swerve wrote:A jar contains 6 red marbles and 9 blue marbles. If Evelyn reaches into the jar and simultaneously draws two marbles at random, what is the probability that she will draw two marbles of the same color?
A. 2/7
B. 12/35
C. 3/7
D. 17/35
E. 25/35
Case 1: 2 green marbles
P(1st marble is green) = 6/15. (Of the 15 marbles, 6 are green.)
P(2nd marble is green) = 5/14. (Of the 14 remaining marbles, 5 are green.)
To combine these probabilities, we multiply:
6/15 * 5/14 =
1/7.
Case 2: 2 red marbles
P(1st marble is red) = 9/15. (Of the 15 marbles, 9 are red.)
P(2nd marble is red) = 8/14. (Of the 14 remaining marbles, 8 are red.)
To combine these probabilities, we multiply:
9/15 * 8/14 =
12/35.
Since a good outcome will be yielded by Case 1 or Case 2, we ADD the fractions in blue:
1/7 + 12/35 = 5/35 + 12/35 = 17/35.
The correct answer is
D.
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