In a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four correct answers just by guessing?

Q.26 In a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four correct answers just by guessing?

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(\frac{10}{243}\)

Let \(X\) = number of correct answers. Each guess is correct with probability \(p = \frac{1}{3}\), so \(q = \frac{2}{3}\), and \(n = 5\). Thus \(X \sim B\left(5, \frac{1}{3}\right)\) and \(P(X = x) = {}^5C_x\left(\frac{1}{3}\right)^x\left(\frac{2}{3}\right)^{5 - x}\).

\(P(X = 4) = {}^5C_4\left(\frac{1}{3}\right)^4\left(\frac{2}{3}\right) = 5\cdot\frac{1}{81}\cdot\frac{2}{3} = \frac{10}{243}\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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In a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four correct answers just by guessing?

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