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Two airplanes A and B bomb a target in succession. The probabilities

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Two airplanes A and B bomb a target in succession. The probabilities  [#permalink]

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New post 18 May 2019, 11:51
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Two airplanes A and B bomb a target in succession. The probabilities of A and B scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. Find the probability that the second plane hits the target.

A. 0.06
B. 0.14
C. 0.32
D. 0.7
E. 0.5

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Re: Two airplanes A and B bomb a target in succession. The probabilities  [#permalink]

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New post 18 May 2019, 22:13
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It’s a question of successive probability.
It will be a infinite G.P .
First Case : When plane A miss and plane B hit - 0.7 * 0.2 => 0.14

Second case : When plane A miss first time and plane B also miss then plane A miss second time and plane B hit at second attempt.

=> 0.7*0.8 * 0.7 * 0.2 => 0.56 * 0.14

Like this it will on
Third case : => 0.56 * 0.56 * 0.14

Sum of all cases => 0.14 + 0.56 *0.14 + 0.56^2 *0.14 ....
0.14 (1 + 0.56 + 0.56^2+ .......)
It’s a infinite G.P with a = 0.14 and r = 0.56

S = a/ 1-r => 0.14/1-0.56
=> 0.14/0.44 => 14/44 => 7/22 => 0.32

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Re: Two airplanes A and B bomb a target in succession. The probabilities  [#permalink]

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New post 18 May 2019, 14:09
DisciplinedPrep wrote:
Two airplanes A and B bomb a target in succession. The probabilities of A and B scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. Find the probability that the second plane hits the target.

A. 0.06
B. 0.14
C. 0.32
D. 0.7
E. 0.5


DisciplinedPrep : are you sure option C 0.32 or is it 0.38?

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Re: Two airplanes A and B bomb a target in succession. The probabilities  [#permalink]

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New post 11 Aug 2019, 21:50
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This needs a language fix. 'In succession' can simply mean one after the other, so A followed by B. Doesn't mean infinitely till the target is hit. Based on current language I feel it should be B
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Re: Two airplanes A and B bomb a target in succession. The probabilities   [#permalink] 11 Aug 2019, 21:50
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