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Probability that X and Y solve

This topic has 4 expert replies and 1 member reply
LulaBrazilia Master | Next Rank: 500 Posts Default Avatar
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Probability that X and Y solve

Post Mon Mar 17, 2014 8:30 am
Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2, and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A) 11/8

B) 7/8

C) 9/64

D) 5/64

E) 3/64

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Top Reply
Post Tue Jul 28, 2015 2:11 pm
LulaBrazilia wrote:
Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2, and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A) 11/8

B) 7/8

C) 9/64

D) 5/64

E) 3/64
P(Z solves the problem) = 1 - P(Z doesn't solve the problem)
So, 5/8 = 1 - P(Z doesn't solve the problem)
So, P(Z doesn't solve the problem) = 3/8

The question asks us to find P(Xavier and Yvonne solve problem, but Zelda does not solve problem)
So, we want: P(X solves problem AND Y solves problem AND Z does not solve)
= P(X solves problem) x P(Y solves problem) x P(Z does not solve)
= 1/4 x 1/2 x 3/8
= 3/64
= E

Cheers,
Brent

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nikhilgmat31 Legendary Member Default Avatar
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Top Reply
Post Tue Jul 28, 2015 11:57 pm
1/4 * 1/2 * (1-5/8)

1/8 * 3/8

=3/64
E

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Post Tue Jul 28, 2015 2:11 pm
LulaBrazilia wrote:
Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2, and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A) 11/8

B) 7/8

C) 9/64

D) 5/64

E) 3/64
P(Z solves the problem) = 1 - P(Z doesn't solve the problem)
So, 5/8 = 1 - P(Z doesn't solve the problem)
So, P(Z doesn't solve the problem) = 3/8

The question asks us to find P(Xavier and Yvonne solve problem, but Zelda does not solve problem)
So, we want: P(X solves problem AND Y solves problem AND Z does not solve)
= P(X solves problem) x P(Y solves problem) x P(Z does not solve)
= 1/4 x 1/2 x 3/8
= 3/64
= E

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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nikhilgmat31 Legendary Member Default Avatar
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Post Tue Jul 28, 2015 11:57 pm
1/4 * 1/2 * (1-5/8)

1/8 * 3/8

=3/64
E

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GMAT/MBA Expert

Post Tue Jul 28, 2015 1:59 pm
LulaBrazilia wrote:
Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2, and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A) 11/8

B) 7/8

C) 9/64

D) 5/64

E) 3/64
Solution:

We are first given the individual probabilities that Xavier, Yvonne, and Zelda WILL solve the problem. We list these probabilities below:

P(Xavier will solve) = ¼

P(Yvonne will solve) = ½

P(Zelda will solve) = 5/8

However, we see the question asks for the probability that Xavier and Yvonne, but not Zelda, will solve the problem.

Thus, we must first determine the probability that Zelda WILL NOT solve the problem. "Solving" and "not solving" are complementary events. When two events are complementary, knowing the probability that one event will occur allows us to calculate the probability that the complement will occur. That is, P(A) + P(Not A) = 1. In the case of Zelda, the probability that she WILL NOT solve the problem, is the complement of the probability that she WILL solve the problem.

P(Zelda will solve) + P(Zelda will not solve) = 1

5/8 + P(Zelda will not solve) = 1

P(Zelda will not solve) = 1 - 5/8 = 3/8

Now we can determine the probability that Xavier and Yvonne, but not Zelda, will solve the problem. Since we need to determine three events that all must take place, we multiply their probabilities together. Thus, we have:

P(Xavier will solve) x P(Yvonne will solve) x P(Zelda will not solve)

¼ x ½ x 3/8

1/8 x 3/8 = 3/64

The answer is E

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