BECE Mathematics 2018 Paper

Concept:Probability is the ratio of favourable outcomes to the total number of possible outcomes.Explanation:The random selection is from $1$ to $20$, so the total number of possible outcomes is $20$.A number divisible by $3$ is a multiple of $3$.The multiples of $3$ from $1$ to $20$ are $3, 6, 9, 12, 15, 18$.Thus, the number of favourable outcomes is $6$.Using the probability formula:$$\text{Probability} = \frac{\text{Favourable outcomes}}{\text{Total outcomes}} = \frac{6}{20}$$Simplify the fraction by dividing numerator and denominator by $2$:$$\frac{6}{20} = \frac{3}{10}$$Answer:The probability that the selected number is divisible by $3$ is $\frac{3}{10}$.Therefore, the correct option is C. $\frac{3}{10}$.