Probability
Independent Trials and Bernoulli Trials
Grade 12
Question:
<p>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:</p>
Step-by-Step Solution
Key Concept: Find min n such that P(X >= 3) >= 0.95 for X ~ Bin(n, 0.75).
<p>P(X >= 3) = 1 - [P(0) + P(1) + P(2)] >= 0.95. Testing n = 6 gives P(X <= 2) approx 0.075 (fails for n=5).</p>
Correct Answer: 6