SOLUTION: Gunman shoots 10 targets two times each with accuracy of 0.63 with each shot. What is the probability of him hitting exactly 4 targets in both shots? What is the probability of him

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Question 1192328: Gunman shoots 10 targets two times each with accuracy of 0.63 with each shot. What is the probability of him hitting exactly 4 targets in both shots? What is the probability of him hitting exactly 4 targets only once?
Answer by ikleyn(52861) About Me  (Show Source):
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Gunman shoots 10 targets two times each with accuracy of 0.63 with each shot.
(a) What is the probability of him hitting exactly 4 targets in both shots?
(b) What is the probability of him hitting exactly 4 targets only once?
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                        I will solve part  (a),  only.


In part (a), for any of 10 targets, we consider the possible events of two types:


      (1)  both shots are hitting the target,  and/or

      (2)  both shots are out the target.



For event (1), the probability  is  0.63%5E2  for each separate target.

For event (2), the probability is  %281-0.63%29%5E2 = 0.37%5E2  for each separate target.



Then the probability to hit 4 of 10 targets exactly twice is 

    P = C%5B10%5D%5E4%2A%280.63%5E2%29%5E4%2A%280.37%5E2%29%5E6 = 210%2A0.63%5E8%2A0.37%5E12 = 3.43%2A10%5E%28-5%29.    ANSWER

Solved.