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21 Jan 2024, 13:24
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C
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Four men and four women participated in a dance competition. Top three performers were awarded a gold coin, a silver coin, and a bronze coin, respectively. If there were no ties, what is the probability that at least two women were awarded?
A. 1/4
B. 1/3
C. 1/2
D. 3/4
E. 4/5
A. 1/4
B. 1/3
C. 1/2
D. 3/4
E. 4/5
21 Jan 2024, 14:04
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udit0610
- P(at least two women) = P(two women) + P(three women) =
= 4C2*4C1/8C3 + 4C3/8C3 =
= 6*4/56 + 4/56 =
= 1/2.
Answer: C.
Alternatively, note that we can have the following four cases:
- WWW
WWM
WMM
MMM
We need to find the combined probability of the green events. Since there are an equal number of men and women, because of the symmetry, the probability of the green events equals the probability of the red events. And since their sum is 1, then the probability of each, red and green events, is 1/2.
Answer: C.
