Probability
Independent Trials and Bernoulli Trials
Grade Class 11
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>
<div class="key-concept"><strong>Key Concept:</strong> Find min n such that P(X >= 3) >= 0.95 for X ~ Bin(n, 0.75).</div>
<div class="trap-box"><strong>Trap:</strong> n=6 is the minimum.</div>
Correct Answer: 6