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A certain type of missile hits the target with probability $\mathrm{p}=0.3$. What is the least number of missiles should be fired so that there is at least an $80 \%$ probability that the target is hit?
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The correct answer is:
5
Probability of hitting the target $=0.3$ If'n' is the no. of times that the Missile is fired. $\therefore$ Probability ofhitting at least once $=1-[1-0.3]^{\mathrm{n}}=0.8$ $0.7^{\mathrm{n}}=0.2$
$n \log 0.7=\log 0.2$
$\Rightarrow \mathrm{n}=4.512$
for $\mathrm{n}=4 ; \mathrm{p} < 0.8$
take $\mathrm{n}=5$
$n=5$
Hence 5 missiles should be fired so that there is at least $80 \%$ prob. that the target is hit.
$n \log 0.7=\log 0.2$
$\Rightarrow \mathrm{n}=4.512$
for $\mathrm{n}=4 ; \mathrm{p} < 0.8$
take $\mathrm{n}=5$
$n=5$
Hence 5 missiles should be fired so that there is at least $80 \%$ prob. that the target is hit.
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