The probability of guessing the correct answer of a certain test question is $\dfrac{x}{12}$. If the probability of not guessing the correct answer is $\dfrac{2}{3}$, then find the value of $x$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
Let the probability of guessing the correct answer be $P(E) = \dfrac{x}{12}$.
Given: $P(\bar{E}) = \dfrac{2}{3}$
Using the complementary events formula:
$$P(E) + P(\bar{E}) = 1$$
$$\frac{x}{12} + \frac{2}{3} = 1$$
$$\frac{x}{12} = 1 - \frac{2}{3} = \frac{1}{3}$$
$$x = \frac{12}{3} = 4$$
Therefore, $x = 4$.
Source: Chapter 14, Section 14.1 — Probability: A Theoretical Approach
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Explanation
- The key formula here is $P(E) + P(\bar{E}) = 1$ (complementary events).
- Substitute the given values and solve for $x$ algebraically — show each step clearly for full marks.
- Examiners award 1 mark for correct use of the complementary formula and 1 mark for the correct value of $x$.