In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten (if sampling is with replacement) is: - Mathematics MCQ Mathematics Mock Test - 6 2026 | ExamTest.live

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In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten (if sampling is with replacement) is:

Solution & Step-by-step Explanation

Probability of a rotten egg (p) = \frac{10}{100} = \frac{1}{10} .Probability of a fresh egg (q) = 1 - p = \frac{9}{10} .Number of trials (n) = 5 .We want the probability of 0 rotten eggs (r = 0 successes): P (X = 0) = (r n) q^{n - r} p^{r} P (X = 0) = (0 5) (\frac{9}{10})^{5} (\frac{1}{10})^{0} = 1 \cdot (\frac{9}{10})^{5} \cdot 1 = (\frac{9}{10})^{5}

Try it yourself before checking the explanation above.

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten (if sampling is with replacement) is:

(1/10)^{5}

(1/5)^{5}

(9/5)^{5}

(9/10)^{5}

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