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# Probability - GMAT Practice Questions

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Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 8

Kudos [?]: 171 [0], given: 50

Probability - GMAT Practice Questions [#permalink]

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27 Aug 2010, 19:39
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Difficulty:

35% (medium)

Question Stats:

59% (01:31) correct 41% (00:45) wrong based on 17 sessions

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Question: James and Colleen are playing basketball. The probability of James missing a shot is x, and the probability of Colleen not making a shot is y. If they each take 2 shots. What is the probability that they both make at least 1 shot apiece?

A) $$1 - (x^2*y^2)$$
B) $$(1-x^2) (1-y^2)$$
C) $$(1-(1-x)^2) (1- (1-y)^2)$$
D) $$(1-(1-x)^2) ((1-y)^2)$$
E) $$(1-(1-y^2)) (1-x^2)$$

I could not solve this problem and I wanted to arrive at the answer using the algebraic route and by not picking numbers.
[Reveal] Spoiler: OA

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GMAT Tutor
Joined: 24 Jun 2008
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Re: Probability - GMAT Practice Questions [#permalink]

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27 Aug 2010, 20:35
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Expert's post
ezhilkumarank wrote:
Question: James and Colleen are playing basketball. The probability of James missing a shot is x, and the probability of Colleen not making a shot is y. If they each take 2 shots. What is the probability that they both make at least 1 shot apiece?

A) $$1 - (x^2*y^2)$$
B) $$(1-x^2) (1-y^2)$$
C) $$(1-(1-x)^2) (1- (1-y)^2)$$
D) $$(1-(1-x)^2) ((1-y)^2)$$
E) $$(1-(1-y^2)) (1-x^2)$$

I could not solve this problem and I wanted to arrive at the answer using the algebraic route and by not picking numbers.

The probability James misses both shots is x*x = x^2. So the probability James makes at least one shot is 1 - x^2. Similarly, the probability Colleen makes at least one shot is 1 - y^2. To find the probability they both make at least one shot, we multiply the probability that each makes at least one shot: (1 - x^2)(1 - y^2).
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 8

Kudos [?]: 171 [0], given: 50

Re: Probability - GMAT Practice Questions [#permalink]

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27 Aug 2010, 21:16
IanStewart wrote:
ezhilkumarank wrote:
Question: James and Colleen are playing basketball. The probability of James missing a shot is x, and the probability of Colleen not making a shot is y. If they each take 2 shots. What is the probability that they both make at least 1 shot apiece?

A) $$1 - (x^2*y^2)$$
B) $$(1-x^2) (1-y^2)$$
C) $$(1-(1-x)^2) (1- (1-y)^2)$$
D) $$(1-(1-x)^2) ((1-y)^2)$$
E) $$(1-(1-y^2)) (1-x^2)$$

I could not solve this problem and I wanted to arrive at the answer using the algebraic route and by not picking numbers.

The probability James misses both shots is x*x = x^2. So the probability James makes at least one shot is 1 - x^2. Similarly, the probability Colleen makes at least one shot is 1 - y^2. To find the probability they both make at least one shot, we multiply the probability that each makes at least one shot: (1 - x^2)(1 - y^2).

Thanks IanStewart. +1 from me.
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Re: Probability - GMAT Practice Questions   [#permalink] 27 Aug 2010, 21:16
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