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JEE Main & Advanced AIEEE Solved Paper-2007

  • question_answer
    Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 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       AIEEE  Solved  Paper-2007

    A)  0.06      

    B)         0.14      

    C)         0.2        

    D)         0.7

    Correct Answer: D

    Solution :

    Firstly, find the probability of incorrect target. Let the events A = 1st aeroplane hit the target, B = 2nd aeroplane hit the target and their corresponding probabilities are \[p(A)=0.3\]and\[p(B)=0.2\] \[p(\overline{A})=0.7\]and\[p(\overline{B})=0.8\] The desired probability \[=P(\overline{A})P(B)+P(\overline{A})P(\overline{B})P(\overline{A})P(B)+....\] \[=(0.7)(0.2)+(0.7)(0.8)(0.7)(0.2)\] \[+(0.7)(0.8)(0.7)(0.8)(0.7)(0.2)+...\] \[=0.14[1+(0.56)+{{(0.56)}^{2}}+...]\] \[=0.14\left[ \frac{1}{1-0.56} \right]=\frac{0.14}{0.44}=\frac{7}{22}=0.32\] From above, it is clear that no option is correct.


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