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The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is_____.please write the full solutioncorrect solution will be marked as brainliest answer |
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Answer» Answer: Correct option is A 6 P=0.75= 4 and q= 4 1
PROBABILITY (of destroying TARGET) ≥0.95 n C 3 ( 4 3 ) 3 ( 4 1 ) n−3 + n C 4 ( 4 3 ) 4 ( 4 1 ) n−4 +...+ n C n ( 4 3 ) n ( 4 1 ) 0 ≥ 100 95
⇒1−{ n C 0 ( 4 3 ) 0 ( 4 1 ) n + n C 1 ( 4 3 ) 1 ( 4 1 ) n−1 + n C 2 ( 4 3 ) 2 ( 4 1 ) n−2 }≥ 100 95
⇒1− 100 95 ≥ 4 n
1 + 4 n
3n + 2.4 n
9n(n−1)
⇒ 20 1 ≥ 2.4 n
2+6n+9n 2 −9n
⇒ 20 2 2n+1
≥2−3n+9n 2
⇒2 2n−1 ≥10−15n+45n 2
n=6 SATISFY the condition So minimum value of n=6 |
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