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An anti aircraft gun can fire four shots at a time. If the probabiliti

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GMATinsight
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An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   25 Oct 2016, 08:42
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An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?


(A) 0.084
(B) 0.916
(C) 0.036
(D) 0.964
(E) 0.92



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BrentGMATPrepNow
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An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   Updated on: 02 Apr 2020, 08:05
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GMATinsight wrote:
An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?

(A) 0.084
(B) 0.916
(C) 0.036
(D) 0.964
(E) 0.92


So, we want P(at least one shot hits the aircraft)

When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(at least 1 shot hits plane) = 1 - P(zero shots hit plane)

P(zero shots hit plane)
P(zero shots hit plane) = P(1st shot misses AND 2nd shot misses AND 3rd shot misses AND 4th shot misses)
= P(1st shot misses) x P(2nd shot misses) x P(3rd shot misses) x P(4th shot misses)
= 0.3 x 0.4 x 0.5 x 0.6
= 3/10 x 4/10 x 5/10 x 6/10
= 360/10000
= 0.036

So.......
P(at least 1 shot hits plane) = 1 - P(zero shots hit plane)
= 1 - 0.036
= 0.964
Answer:
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D

Originally posted by BrentGMATPrepNow on 25 Oct 2016, 09:17.
Last edited by BrentGMATPrepNow on 02 Apr 2020, 08:05, edited 1 time in total.
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Re: An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   25 Oct 2016, 09:18
Sum of probabilities of each shot= 0.7+0.3*0.6+0.3*0.4*0.5+0.3*0.4*0.5*0.4

=0.964

IMO D


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Re: An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   25 Oct 2016, 16:24
Although the answers make sense, I feel like this question is missing info. Isn't a pretty big assumption that one shot is enough to bring the aircraft down? Have yet to see a Quant question that makes that big a leap without providing the info in the prompt.
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Re: An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   25 Oct 2016, 16:36
Character wrote:
Although the answers make sense, I feel like this question is missing info. Isn't a pretty big assumption that one shot is enough to bring the aircraft down? Have yet to see a Quant question that makes that big a leap without providing the info in the prompt.


Even I had the same doubt. I think question has to be rephrased as "What is the probability of hitting the aircraft by at least one of the shots?"


Experts please share your thoughts.


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Re: An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   25 Oct 2016, 16:51
acegmat123 wrote:
Character wrote:
Although the answers make sense, I feel like this question is missing info. Isn't a pretty big assumption that one shot is enough to bring the aircraft down? Have yet to see a Quant question that makes that big a leap without providing the info in the prompt.


Even I had the same doubt. I think question has to be rephrased as "What is the probability of hitting the aircraft by at least one of the shots?"


Experts please share your thoughts.




Definitely phrased wrong. I'm weaker in quant but I'm 99th percentile in V and this would scream assumption issue on a CR question.
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Re: An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   25 Oct 2016, 17:53
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Character wrote:
Although the answers make sense, I feel like this question is missing info. Isn't a pretty big assumption that one shot is enough to bring the aircraft down? Have yet to see a Quant question that makes that big a leap without providing the info in the prompt.


Agreed. I had the same doubt. I just worked backwards from the answer.
An official GMAT question would not have such ambiguity.
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Re: An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink] New post   29 Aug 2021, 00:36
1- Prob(All misses from four shots) = 1-0.3*0.4*0.5*0.6 = 1-0.036 = 0.964
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Re: An anti aircraft gun can fire four shots at a time. If the probabiliti [#permalink]
29 Aug 2021, 00:36
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