Question 1192328
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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.



<pre>
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  {{{0.63^2}}}  for each separate target.

For event (2), the probability is  {{{(1-0.63)^2}}} = {{{0.37^2}}}  for each separate target.



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

    P = {{{C[10]^4*(0.63^2)^4*(0.37^2)^6}}} = {{{210*0.63^8*0.37^12}}} = {{{3.43*10^(-5)}}}.    <U>ANSWER</U>
</pre>

Solved.