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

There are 10% defective items in a large bulk of items. What is the probability that a sample of 4 items will include not more than one defective item?

Q.6 (B)(ii) There are 10% defective items in a large bulk of items. What is the probability that a sample of 4 items will include not more than one defective item?

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

1 answer

Best answer

Answer: 0.9477

Let \(X\) be the number of defective items in the sample. Then \(X \sim B(n = 4, p = 0.1)\), \(q = 0.9\), and \(P(X = x) = {}^4C_x(0.1)^x(0.9)^{4 - x}\), \(x = 0, 1, 2, 3, 4\).

\(P(X \le 1) = P(X = 0) + P(X = 1)\)

\(= {}^4C_0(0.9)^4 + {}^4C_1(0.1)(0.9)^3 = 0.6561 + 4(0.1)(0.729) = 0.6561 + 0.2916 = 0.9477\)

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

Was this answer helpful?

There are 10% defective items in a large bulk of items. What is the probability that a sample of 4 items will include not more than one defective item?

1 answer

Your answer