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# Adam and Bob shoot a target in succession. The probability

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VP
Joined: 20 Jul 2017
Posts: 1329
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)

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Updated on: 22 Jan 2020, 22:54
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

22% (02:29) correct 78% (01:40) wrong based on 41 sessions

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Adam and Bob shoot a target in succession until someone hits the target. The probability of Adam and Bob hitting the target is 0.25 and 0.20 respectively. Bob will shoot only if Adam misses the target. The probability that Bob hits the target is?

A. 0.15
B. 0.25
C. 0.375
D. 0.45
E. 0.75

Posted from my mobile device

Originally posted by Dillesh4096 on 10 Jan 2020, 09:36.
Last edited by Dillesh4096 on 22 Jan 2020, 22:54, edited 1 time in total.
VP
Joined: 19 Oct 2018
Posts: 1304
Location: India
Re: Adam and Bob shoot a target in succession. The probability  [#permalink]

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10 Jan 2020, 10:02
1
Probability that Bob hits target in first chance= $$\frac{3}{4}*\frac{1}{5}= \frac{3}{20}$$ = $$0.15$$

Probability that Bob hits target in second chance= $$\frac{3}{4}*\frac{4}{5} * \frac{3}{4} * \frac{1}{5}$$ = $$\frac{3}{20} * \frac{3}{5}$$= $$0.15*0.6$$

Probability that Bob hits target in third chance= $$\frac{3}{4}*\frac{4}{5} * \frac{3}{4} * \frac{4}{5} * \frac{3}{4} * \frac{1}{5} = \frac{3}{20} * (\frac{3}{5})^2= 0.15*(0.6)^2$$
and so on

probability that Bob hits the target is= $$0.15 + 0.15*0.6 + 0.15*(0.6)^2+.....$$ {sum of infinite GP}

= $$\frac{a}{1-r}$$ = $$\frac{0.15}{1-0.6} = 0.375$$

Dillesh4096 wrote:
Adam and Bob shoot a target in succession. The probability of Adam and Bob hitting the target is 0.25 and 0.20 respectively. Bob will shoot only if Adam misses the target. The probability that Bob hits the target is?

A. 0.15
B. 0.25
C. 0.375
D. 0.45
E. 0.75

Posted from my mobile device
Intern
Joined: 16 Dec 2019
Posts: 17
Re: Adam and Bob shoot a target in succession. The probability  [#permalink]

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22 Jan 2020, 04:46
nick1816 wrote:
Probability that Bob hits target in first chance= $$\frac{3}{4}*\frac{1}{5}= \frac{3}{20}$$ = $$0.15$$

Probability that Bob hits target in second chance= $$\frac{3}{4}*\frac{4}{5} * \frac{3}{4} * \frac{1}{5}$$ = $$\frac{3}{20} * \frac{3}{5}$$= $$0.15*0.6$$

Probability that Bob hits target in third chance= $$\frac{3}{4}*\frac{4}{5} * \frac{3}{4} * \frac{4}{5} * \frac{3}{4} * \frac{1}{5} = \frac{3}{20} * (\frac{3}{5})^2= 0.15*(0.6)^2$$
and so on

probability that Bob hits the target is= $$0.15 + 0.15*0.6 + 0.15*(0.6)^2+.....$$ {sum of infinite GP}

= $$\frac{a}{1-r}$$ = $$\frac{0.15}{1-0.6} = 0.375$$

Dillesh4096 wrote:
Adam and Bob shoot a target in succession. The probability of Adam and Bob hitting the target is 0.25 and 0.20 respectively. Bob will shoot only if Adam misses the target. The probability that Bob hits the target is?

A. 0.15
B. 0.25
C. 0.375
D. 0.45
E. 0.75

Posted from my mobile device

Since the question asks the probability of Bob hitting the target, isn't it understood that it's asking for the first attempt ?
VP
Joined: 20 Jul 2017
Posts: 1329
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Adam and Bob shoot a target in succession. The probability  [#permalink]

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22 Jan 2020, 22:01
1
allkagupta wrote:
Since the question asks the probability of Bob hitting the target, isn't it understood that it's asking for the first attempt ?

Hi allkagupta

That's where the exam gets tricky, you cannot assume anything if NOT given in the question.
GMAT will try to trick you with the wordings.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 2012
Re: Adam and Bob shoot a target in succession. The probability  [#permalink]

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22 Jan 2020, 22:45
1
Dillesh4096 wrote:
That's where the exam gets tricky, you cannot assume anything if NOT given in the question.
GMAT will try to trick you with the wordings.

No, that's not the case. GMAT questions are always precisely worded; the exam is never trying to trick you with the wording of a question, and you will never be left guessing, on an official question, what mathematical situation you are meant to investigate. In the problem above, you are left to guess: what happens if Adam misses the target and then Bob misses the target? Clearly if the answer is C, the intention is that they both shoot again until someone hits the target, but I'd never guess that's the intention from the way the question is phrased. As it's written, I'd guess that Adam shoots, and then if he misses, Bob shoots, and that's the end of the shooting. So the question is not worded the way a real GMAT question would be.

You also never need to sum infinite sequences on the GMAT (since calculus is required to be sure infinite sums converge, and calculus is out of the scope of the test) so this is not a realistic problem.
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VP
Joined: 20 Jul 2017
Posts: 1329
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Adam and Bob shoot a target in succession. The probability  [#permalink]

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22 Jan 2020, 22:53
IanStewart wrote:
No, that's not the case. GMAT questions are always precisely worded; the exam is never trying to trick you with the wording of a question, and you will never be left guessing, on an official question, what mathematical situation you are meant to investigate. In the problem above, you are left to guess: what happens if Adam misses the target and then Bob misses the target? Clearly if the answer is C, the intention is that they both shoot again until someone hits the target, but I'd never guess that's the intention from the way the question is phrased. As it's written, I'd guess that Adam shoots, and then if he misses, Bob shoots, and that's the end of the shooting. So the question is not worded the way a real GMAT question would be.

You also never need to sum infinite sequences on the GMAT (since calculus is required to be sure infinite sums converge, and calculus is out of the scope of the test) so this is not a realistic problem.

Hi IanStewart,

Agree with you about the highlighted part, editing the question.
Thanks!
Intern
Joined: 16 Dec 2019
Posts: 17
Re: Adam and Bob shoot a target in succession. The probability  [#permalink]

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23 Jan 2020, 02:44
IanStewart wrote:
Dillesh4096 wrote:
That's where the exam gets tricky, you cannot assume anything if NOT given in the question.
GMAT will try to trick you with the wordings.

No, that's not the case. GMAT questions are always precisely worded; the exam is never trying to trick you with the wording of a question, and you will never be left guessing, on an official question, what mathematical situation you are meant to investigate. In the problem above, you are left to guess: what happens if Adam misses the target and then Bob misses the target? Clearly if the answer is C, the intention is that they both shoot again until someone hits the target, but I'd never guess that's the intention from the way the question is phrased. As it's written, I'd guess that Adam shoots, and then if he misses, Bob shoots, and that's the end of the shooting. So the question is not worded the way a real GMAT question would be.

You also never need to sum infinite sequences on the GMAT (since calculus is required to be sure infinite sums converge, and calculus is out of the scope of the test) so this is not a realistic problem.

Thanks a ton. For a moment I was questioning my entire understanding of questions on the GMAT.
Thanks again to make this point clear
Intern
Joined: 13 Jan 2020
Posts: 18
Re: Adam and Bob shoot a target in succession. The probability  [#permalink]

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28 Jan 2020, 21:36
Probability of Bob hitting the target in
first chance$$= \frac{3}{4}∗\frac{1}{5} = \frac{3}{20} = 0.15$$

third chance$$= \frac{3}{4}∗\frac{4}{5}∗\frac{3}{4}∗\frac{4}{5}∗\frac{3}{4}∗\frac{1}{5}=\frac{3}{20}∗(\frac{3}{5})^2=0.15∗(0.6)^2$$
and so on ..

Bob hits the target is $$= 0.15+0.15∗0.6+0.15∗(0.6)^2+.....$${ infinite GP}

$$= \frac{0.15}{(1−0.6)} = 0.375$$

Option C
Re: Adam and Bob shoot a target in succession. The probability   [#permalink] 28 Jan 2020, 21:36
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