Chapter: Probability Distributions· Mathematics & Statistics (Commerce) Part 2

The eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg in the lot of 10 eggs.

Q.6 (A)(iii) The eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg in the lot of 10 eggs.

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

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Answer: \(P(X \ge 1) = 1 - \left(\dfrac{9}{10}\right)^{10} \approx 0.6513\)

Let X = number of defective eggs among the 10 drawn. Since the draws are with replacement, the trials are independent with \(p = 0.1\), \(q = 0.9\), \(n = 10\), so \(X \sim B(10, 0.1)\) and \(P(X = x) = {}^{10}C_x (0.1)^x (0.9)^{10-x}\).

\(P(X \ge 1) = 1 - P(X = 0) = 1 - (0.9)^{10} = 1 - \left(\dfrac{9}{10}\right)^{10}\).

Since \((0.9)^{10} \approx 0.3487\), the required probability \(\approx 0.6513\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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The eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg in the lot of 10 eggs.

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