Theory question 106
ProbabilityA bag contains 24 mangoes out of which six are bad. If 6 mangoes are selected randomly from the bag with replacement, find the probability that not more than 3 are bad.
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Model answer
P(bad) = 6/24 = ¼, P(good) = ¾, n = 6.
P(X ≤ 3) = 1 − [P(4) + P(5) + P(6)].
P(4) = 15(¼)⁴(¾)² = 135/4096; P(5) = 6(¼)⁵(¾) = 18/4096; P(6) = 1/4096.
P(X ≤ 3) = 1 − 154/4096 = 3942/4096 ≈ 0.962.
Explanation
It's quicker to subtract the 4, 5 and 6 cases from 1.