JAMB Mathematics 2015 Paper

Concept:The addition rule of probability connects the union of two events to their intersection.Explanation:Let $P(A) = \frac{1}{6}$, $P(B) = \frac{1}{4}$, and $P(A \cup B) = \frac{1}{12}$.The formula for the probability of $A$ or $B$ or both is:$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$Rearrange to find the probability of both outcomes occurring:$$P(A \cap B) = P(A) + P(B) - P(A \cup B)$$Substitute the given values:$$P(A \cap B) = \frac{1}{6} + \frac{1}{4} - \frac{1}{12}$$Convert to a common denominator of $12$:$$= \frac{2}{12} + \frac{3}{12} - \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$$Answer:The probability of both outcomes $A$ and $B$ is $\frac{1}{3}$, which is option B.