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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
for each separate target.
For event (2), the probability is
=
for each separate target.
Then the probability to hit 4 of 10 targets exactly twice is
P =
=
=
. ANSWER
Solved.