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# James and Colleen are playing basketball. The probability of James mis

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James and Colleen are playing basketball. The probability of James mis  [#permalink]

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27 Aug 2010, 19:39
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51% (01:39) correct 49% (01:59) wrong based on 59 sessions

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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.

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Re: James and Colleen are playing basketball. The probability of James mis  [#permalink]

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27 Aug 2010, 20:35
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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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Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 327
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: James and Colleen are playing basketball. The probability of James mis  [#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: James and Colleen are playing basketball. The probability of James mis  [#permalink]

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20 Oct 2019, 05:13
Could someone tell me how the solution would change if the question asked for the probability that both make exactly one shot?
Re: James and Colleen are playing basketball. The probability of James mis   [#permalink] 20 Oct 2019, 05:13
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