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Question
Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that exactly 2 will strike the target .
Solution
Let X be the number of bombs that hit the target.
Then, X follows a binomial distribution with n = 6
Let p be the probability that a bomb dropped from an aeroplane will strike the target.
\[\therefore p = 0 . 2 \text{ and } q = 0 . 8\]
\[\text{ Hence, the distribution is given by } \]
\[P(X = r) = ^{6}{}{C}_r \left( 0 . 2 \right)^r \left( 0 . 8 \right)^{6 - r} \]
P \[(\text{ exactly 2 will strike the target } ) = P(X = 2) \]
\[ = ^{6}{}{C}_2 (0 . 2 )^2 (0 . 8 )^4 \]
\[ = 15(0 . 04)\left( 0 . 4096 \right)\]
\[ = 0 . 2458\]
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