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September 17th, 2013, 08:24 AM  #1 
Member Joined: Oct 2011 Posts: 81 Thanks: 0  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. 
September 17th, 2013, 08:37 AM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: A probability question
Do you know what order they fire? Is it A fires first, then B, then C?

September 17th, 2013, 09:12 AM  #3 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  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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