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September 17th, 2013, 08:24 AM   #1
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A probability question

Question-
A,B,C are three persons having a gun. A is targeting to B, B and C are targeting to A. Probability of hitting the target by A,B,C are 2/3, 1/2, 1/3 respectively. If A is hit then find the probability that B hits him and not C.

I approached the question by Bayes' theorem but did not go too far.
Any help would be appreciated.
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September 17th, 2013, 08:37 AM   #2
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Re: A probability question

Do you know what order they fire? Is it A fires first, then B, then C?
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September 17th, 2013, 09:12 AM   #3
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Re: A probability question

Assuming they shoot in alphabetic order, what happens is:

1) 2/3 of the time A shoots B; so B is dead; then in 1/3 of these cases C shoots A. So, A gets shot 2/9 by C.

2) 1/3 of the time A misses B:
2.1) 1/2 of theses cases B shoots A. So, A gets shot 1/6 by B.
2.2) 1/2 of these cases B misses A, and in 1/3 of these cases C shoots A. So, A gets shot 1/18 by C.

In total, A gets shot 8/18: 1/6 = 3/18 by B and 5/18 by C.

So, if A gets shot, the probabilty that B shot him is 3/8.
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