Assume that the probability that a bomb dropped from an aeroplane… - Vidyadip

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.
at least 2 will strike the target.

✓

Answer

probabilty that bomb strikes a target p = 0.2
Probability that a bomb misses the target = 0.8
n = 6
let X = number of bombs that strike the target
P(X = 2) = exactly 2 bombs strike the target
$=\text{ }^6\text{C}_2\big(\frac{2}{10}\big)^2\times\big(\frac{8}{10}\big)^4=15\times\frac{16384}{10^6}=0.24576$
$\text{P(X}\geq2)=$ at least 2 bombs strike the target
$=1-\text{P(X}<2)$
$=1-\big[\text{P(X}=0)+\text{P(X=1})\big]$
$=1-\big[\text{ }^6\text{C}_0\big(\frac{2}{10}\big)^0\times\big(\frac{8}{10}\big)^6+\text{ }^6\text{C}_1\big(\frac{2}{10}\big)^1\times\big(\frac{8}{10}\big)^6\big]$
$=1-\big[0.0.262144+0.393216\big]=1-0.65536$
$=0.34464$

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