A bag contains 15 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and

[BTGmoderatorDC]

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?

a) 2/35
b) 1/15
c) 6/35
d) 13/70
e) 1/5



OA C

Source: Veritas Prep

[Jay@ManhattanReview]

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?

a) 2/35
b) 1/15
c) 6/35
d) 13/70
e) 1/5

OA C

Source: Veritas Prep

Probability that she selects the red scarf but not the green scarf is given by

(# of ways to select 1 red and 2 out of 13 scarves) / (# of ways to select 3 out of 15 scarves)

= (1C1*13C1) / (15C3) = [(13.12)/(1.2)] / [(15.14.13)/(1.2.3)] = 6/35

The correct answer: C

Hope this helps!

-Jay
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Manhattan Review

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