Veritas Prep
Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
A. 3/140
B. 1/28
C. 3/56
D. 3/35
E. 7/40
OA E
Alice, Benjamin, and Carol each try independently to win a
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P(exactly 2 win) = P(A wins and B wins and C loses OR B wins and C wins and A loses OR A wins and C wins and B loses)AAPL wrote:Veritas Prep
Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
A. 3/140
B. 1/28
C. 3/56
D. 3/35
E. 7/40
OA E
= P(A wins and B wins and C loses) + P(B wins and C wins and A loses) + P(A wins and C wins and B loses)
Let's calculate each probability
P(A wins and B wins and C loses) = P(A wins) x P(B wins) x P(C loses)
= 1/5 x 3/8 x 5/7
= 15/280
P(B wins and C wins and A loses) = P(B wins) x P(C wins) x P(A loses)
= 3/8 x 2/7 x 4/5
= 24/280
P(A wins and C wins and B loses) = P(A wins) x P(C wins) x P(B loses)
= 1/5 x 2/7 x 5/8
= 10/280
So, P(exactly 2 win) = 15/280 + 24/280 + 10/280
= 49/280
= 7/40
Answer: E
Cheers,
Brent
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We must individually consider each possible outcome of having two winners and one loser.AAPL wrote:Veritas Prep
Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
A. 3/140
B. 1/28
C. 3/56
D. 3/35
E. 7/40
OA E
If Alice and Benjamin win and Carol loses, we have:
1/5 x 3/8 x 5/7 = 1 x 3/8 x 1/7 = 3/56
If Alice and Carol win and Benjamin loses, we have:
1/5 x 5/8 x 2/7 = 1 x 1/8 x 2/7 = 2/56
If Benjamin and Carol win and Alice loses, we have:
4/5 x 3/8 x 2/7 = 1/5 x 3/2 x 2/7 = 1/5 x 3 x 1/7 = 3/35
Therefore, the probability that two of them will win and one will lose is:
3/56 + 2/56 + 3/35 = 15/280 + 10/280 + 24/280 = 49/280 = 7/40
Answer: E
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