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probability medium diff. (600-650)

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by Night reader » Thu Dec 02, 2010 12:07 pm
From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) 1/10
(B) 1/6
(C) 1/5
(D) 1/4
(E) 1/3
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by Rahul@gurome » Thu Dec 02, 2010 12:13 pm
Night reader wrote:From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) 1/10
(B) 1/6
(C) 1/5
(D) 1/4
(E) 1/3
Total number of ways to select 4 students from 6 = 6C4 = 15

Possible selection such that more juniors than sophomores are selected,
  • 3 junior, 1 sophomore
    1 sophomore out of 3 can be selected in 3 ways.
    Thus total 3 possible selections
Required probability = 3/15 = 1/5

The correct answer is C.
Last edited by Rahul@gurome on Thu Dec 02, 2010 12:17 pm, edited 1 time in total.
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by shovan85 » Thu Dec 02, 2010 12:14 pm
Night reader wrote:From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) 1/10
(B) 1/6
(C) 1/5
(D) 1/4
(E) 1/3
4 students are to be randomly selected in C(6,4) = 15 ways

More juniors to be seleted then 3 Juniors 1 sophomore is the only possibility.

1 S can be selected in C(3,1) = 3 ways and 3 J can be selected in C(3,3) = 1 ways

Thus 3*1/15 = 1/5

IMO C
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