During a war, a plane is sent to drop bombs on a bridge. The pilot knows that a direct hit is required to destroy the bridge. He also knows that each of his bombs has a probability of only 30% of scoring a direct hit. What is the minimum number of bombs he should drop so that his chances of successfully completing his mission are greater than 75%?
Answers
Given : a plane is sent to drop bombs on a bridge. his bombs has a probability of only 30% of scoring a direct hit
To find : minimum number of bombs he should drop so that his chances of successfully completing his mission are greater than 75%
Solution:
Let say minimum number of Bomb dropped = n
Probability of direct hit p = 0.3
probability of not Direct hit q = 1 -0.3 = 0.7
P(x) = ⁿCₓpˣqⁿ⁻ˣ
successfully completing his mission are greater than 75%
=> Hitting 0 Direct hit < 25 %
=> P(0) < 0.25
=> ⁿC₀(0.3)⁰(0.7)ⁿ < 0.25
=> (0.7)ⁿ < 0.25
Taking log both sides
=> n log (0.7) < log (0.25)
=> n > 3.88
Hence n = 4
minimum number of bombs he should drop so that his chances of successfully completing his mission are greater than 75% are 4
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