Two aeroplanes I and II bomb a target in succ | vedclass

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Question

Let the events, $A=$ Ist aeroplane hit the target

$\mathrm{B}=$ IInd aeroplane hit the target

And their corresponding probabilities are

$P(A)

Vedclass · Accepted Answer

$0.32$

Vedclass · Answer

Let the events, $A=$ Ist aeroplane hit the target

$\mathrm{B}=$ IInd aeroplane hit the target

And their corresponding probabilities are

$P(A)=0.3 	ext { and } P(B)=0.2$

$\Rightarrow \quad P(\bar{A})=0.7 \quad$ and $\quad P(\bar{B})=0.8$

$	herefore$ Required probability $=P(\bar{A}) P(B)+P(\bar{A}) P(\bar{B}) P(\bar{A}) P(B)+$

$=(0.7)(0.2)+(0.7)(0.8)(0.7)(0.2)$$+(0.7)(0.8)(0.7)(0.8)(0.7)(02)+. . .$

$=0.14\left[1+(0.56)+(0.56)^{2}+\ldots .ight]$

$=0.14\left(\frac{1}{1-0.56}ight)=\frac{0.14}{0.44}=\frac{7}{22}=0.32$

Two aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $l$ and $II$ scoring a hit correctlyare $0.3$ and $0.2,$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

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