The probability that a bomb will hit the target is 0.8. Using the… - Vidyadip

Question

The probability that a bomb will hit the target is $0.8.$ Using the following activity, find the probability that, out of $5$ bombs, exactly $2$ will miss the target
Solution: Let $p =$ probability that bomb miss the target
$ \therefore q =\square, p =\square, n =5 .$
$X \sim B (5, \square), P ( x )={ }^{ n } C _x P ^x q ^{ n -x}$
$P ( X =2)={ }^5 C _2 \square=\square $

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Answer

Let $p=$ probability that bomb miss the target
$\therefore q = 0 . 8 , p = 0 . 2 , n =5$
$X \sim B (5,0.2), P ( x )={ }^{ n } C _x P ^x q ^{ n -x}$
$P(X=2)={ }^5 C_2( 0 . 2 )^2( 0 . 8 )^3$
$=0.2048$

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