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Tue Dec 07, 2010 5:42 am
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:28) correct
50%
(02:48)
wrong
based on 119
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Two representatives must be selected from each of two groups of students. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
A. 1/6
B. 1/4
C. 2/7
D. 1/3
E. 1/2
A. 1/6
B. 1/4
C. 2/7
D. 1/3
E. 1/2
Tue Dec 07, 2010 6:09 am
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tomchris
Group #1: {m1, m2, m3, w1};
Group #2: {m4, w2, w3}.
There are following cases possible to select 2m and 2w:
Both men from group #1 and both women from group #2: \(C^2_3*C^2_2=3\);
One man and one women from each group: \((C^1_3*C^1_1)*(C^1_1*C^1_2)=6\);
Total ways to select 2 persons from group #1 and group #2 is \(C^2_4*C^2_3=18\);
\(P=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}=\frac{3+6}{18}=\frac{1}{2}\).
Answer: E.
Fri Feb 05, 2016 10:28 am
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tomchris
Group 1: 3 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*1*1*2 = 6 ways
Total Favorable cases = 3+6 = 9
Total Possible ways of selecting students 2 from each group = 4C2*3C2 = 6*3 = 18
Probability = 9/18 = 1/2
Answer : Option E
