The probability that A hits a target is 34. Then the minimum number of attempts A should take so that the probability of hitting the target at least once is at least 0.99, is
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Solution
Let p be the probability of hitting the target. p=34
and q=1−p=14 P(X=x)=nCxpxqn−x
We have to find the smallest n such that P(X≥1)≥0.99⇒1−P(X=0)≥0.99⇒0.01≥nC0(34)0(14)n−0⇒4n≥100
Hence, the minimum value of n is 4.