sud21 wrote:A bag contains 15 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
2/35
1/15
6/35
13/70
1/5
P(exactly n times) = P(one way) * total possible ways.
Let R = the probability of choosing the red scarf and N = the probability of choosing a scarf that is neither red nor green.
P(one way):
ONE WAY to get exactly 1 R and 2 N's is RNN.
P(R on the first pick) = 1/15. (Of the 15 scarves, 1 is red.)
P(N on the 2nd pick) = 13/14. (Of the 14 remaining scarves, 13 are neither red nor green.)
P(N on the 3rd pick) = 12/13. (Of the 13 remaining scarves, 12 are neither red nor green.)
Since we want all of these events to happen, we MULTIPLY:
1/15 * 13/14 * 12/13 = 2/35.
Total possible ways:
RNN is only ONE WAY to get exactly 1 R and 2 N's.
The resulting probability above must be multiplied by ALL OF THE WAYS to get exactly 1 R and 2 N's:
RNN
NRN
NNR.
Total ways = 3.
Multiplying the results above, we get:
P(1 R and 2 N's) = 2/35 * 3 = 6/35.
The correct answer is
C.
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