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25 Mar 2026, 09:50
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B
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Difficulty:
95%
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Question Stats:
41% (02:52) correct
59%
(02:10)
wrong
based on 37
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On the first floor of a building, there are 1 man and 5 women. On the second floor, there are 5 men and 1 woman. Two people are selected at random from each floor. What is the probability that three women are selected?
A. 1/9
B. 2/9
C. 1/3
D. 4/9
E. 1/2
A. 1/9
B. 2/9
C. 1/3
D. 4/9
E. 1/2
29 Mar 2026, 03:11
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Only way to get 3 women = 2 from F1 and 1 from F2.
5c2 = 10, remaining 1 man hence 10 total ways in F1
1c1*5c1 = 5 total ways in F2.
Total ways of choosing = 6c2*6c2 = 15*15 = 225.
Choosing both floors hence
10*5/225 = 2/9.
Answer: Option B
5c2 = 10, remaining 1 man hence 10 total ways in F1
1c1*5c1 = 5 total ways in F2.
Total ways of choosing = 6c2*6c2 = 15*15 = 225.
Choosing both floors hence
10*5/225 = 2/9.
Answer: Option B
kevincan
29 Mar 2026, 03:58
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This is a conditional probability problem. The key insight is figuring out how 3 women get selected when you're picking 2 from each floor.
Floor 1: 1 man, 5 women (6 total)
Floor 2: 5 men, 1 woman (6 total)
Picking 2 from each floor, so 4 total people selected.
For exactly 3 women total, the only possibility is: 2 women from Floor 1 AND 1 woman from Floor 2 (since Floor 2 only has 1 woman, you can't get 2 from there).
1. P(2 women from Floor 1):
C(5,2) / C(6,2) = 10/15 = 2/3
2. P(1 woman from Floor 2, meaning we pick the 1 woman + 1 of the 5 men):
C(1,1) * C(5,1) / C(6,2) = 5/15 = 1/3
3. These events are independent (different floors), so multiply:
P(3 women total) = (2/3) * (1/3) = 2/9
Answer: B
The trap here is not thinking carefully about what "3 women" requires from each floor. Most people who get this wrong either forget to condition on where the women come from, or try to compute it as a single pool of 12 people. Separate the floors and it becomes much cleaner.
Floor 1: 1 man, 5 women (6 total)
Floor 2: 5 men, 1 woman (6 total)
Picking 2 from each floor, so 4 total people selected.
For exactly 3 women total, the only possibility is: 2 women from Floor 1 AND 1 woman from Floor 2 (since Floor 2 only has 1 woman, you can't get 2 from there).
1. P(2 women from Floor 1):
C(5,2) / C(6,2) = 10/15 = 2/3
2. P(1 woman from Floor 2, meaning we pick the 1 woman + 1 of the 5 men):
C(1,1) * C(5,1) / C(6,2) = 5/15 = 1/3
3. These events are independent (different floors), so multiply:
P(3 women total) = (2/3) * (1/3) = 2/9
Answer: B
The trap here is not thinking carefully about what "3 women" requires from each floor. Most people who get this wrong either forget to condition on where the women come from, or try to compute it as a single pool of 12 people. Separate the floors and it becomes much cleaner.
