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Alice, Benjamin, and Carol each try independentl [#permalink]
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31 Oct 2013, 10:18
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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
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Re: Alice, Benjamin, and Carol each try independentl [#permalink]
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31 Oct 2013, 10:25
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Puneethrao wrote: 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 P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40. Answer: E.
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Re: Alice, Benjamin, and Carol each try independentl [#permalink]
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31 Oct 2013, 10:32
Puneethrao wrote: 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 probability that exactly two of the three players will win = probability of (A will win,B will win,C will lose+ A will win , B will lose ,C will win+ A will lose,B will win,C will win) =>(1/5 * 3/8 * (1 2/7)) + (1/5 * (1  3/8) * 2/7) + ((1  1/5) * 3/8 * 2/7) =>15/280 + 10/280 + 24/280 => 49/280 =>7/40



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Alice, Benjamin, and Carol each try independentl [#permalink]
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05 Mar 2015, 10:30
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Well. there are three possible outcomes of interest, if 2 of the three have to win and one to lose:
AB...C AC...B CB...A
For the wins, we use the given probabilities. For the loss we use the remaining of the given probability. We multiply these together:
1/5 * 3/8 * 5/7 = 15 / 280 1/5 * 2/7 * 5/8 = 10 / 280 3/8 * 2/7 * 4/5 = 24 / 280
We now want to add these individual probabilities, which gives us: 49 / 280 = 7 / 40 ANS E



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Re: Alice, Benjamin, and Carol each try independentl [#permalink]
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16 Apr 2017, 19:35
Puneethrao wrote: 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 In order to solve this question we should set up the equation Prob (Exactly #success Exactly # failures)= P(A success x B success x C failure) + P(A success B failure C success) + P(A failure x B success x C success) Prob(Exactly # 2 success and Exactly 1 Failure)= P( 1/5 x 3/8 x 5/7) + P(1/5 x 5/8 x 2/7) + P( 4/5 x 3/8 x 2/7) = 49/280 Thus 7/40



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Re: Alice, Benjamin, and Carol each try independentl [#permalink]
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16 Apr 2017, 20:16
Puneethrao wrote: 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 To solve this question we need to consider three different cases  • A and B wins and C loses • The probability of the above case can be written as 
o \(P(A_wB_wC_L) = \frac{1}{5} * \frac{3}{8} * (1\frac{2}{7}) = \frac{3}{56}\) • B and C wins and A loses • The probability of the above case can be written as 
o \(P(A_LB_wC_w) = (1\frac{1}{5}) * \frac{3}{8} * \frac{2}{7} = \frac{3}{35}\) • C and A wins and B loses • The probability of the above case can be written as 
o \(P(A_wB_LC_w) = \frac{1}{5} * (1\frac{3}{8}) * \frac{2}{7} = \frac{1}{28}\) • The overall probability \(= P(A_wB_wC_L) + P(A_LB_wC_w) + P(A_wB_LC_w)\)
\(= \frac{3}{56} + \frac{3}{35} + \frac{1}{28}\) \(= \frac{3}{56} + \frac{3}{35} + \frac{1}{28}\) \(= \frac{(15+24+10)}{280}\) \(=\frac{7}{40}\) Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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Re: Alice, Benjamin, and Carol each try independentl [#permalink]
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05 Feb 2018, 11:33
Hi All, Since we have the probabilities of each person winning a game, we can 'map out' the 3 situations in which 2 of them win and 1 of them loses: A wins, B wins, C loses = (1/5)(3/8)(5/7) = 15/240 A wins, B loses, C wins = (1/5)(5/8)(2/7) = 10/240 A loses, B wins, C wins = (4/5)(3/8)(2/7) = 24/240 Total probability = 15/280 + 10/280 + 24/280 = 49/280 = 7/40 Final Answer: GMAT assassins aren't born, they're made, Rich
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