In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

Step-by-step solution

Sampling without replacement from a finite population follows a hypergeometric distribution, but given the options, a binomial approximation is expected since one option matches it exactly. The probability of a defective apple is p = 10 100 = 0.1 . Using the binomial distribution with n = 6 trials and k = 3 successes: P(X = 3) = 6 3 p^3 (1-p)³ = 20 (0.1)^3 (0.9)^3 P(X = 3) = 20 0.001 0.729 = 0.01458 This matches option D exactly. Final answer: D