BECE Mathematics 2013 Paper

Concept:Probability is the ratio of favourable outcomes to the total number of equally likely outcomes.Explanation:The sample space is $S = \{1,2,3,4,5,6,7,8,9,10\}$.So the total number of possible outcomes is $|S| = 10$.Odd numbers are not divisible by $2$ without leaving a remainder.From $S$, the odd numbers are $\{1, 3, 5, 7, 9\}$.Thus, the number of favourable outcomes is $5$.Now, using the formula for probability:$$P(\text{odd}) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} = \frac{5}{10}.$$Simplifying, we get:$$\frac{5}{10} = \frac{1}{2}.$$Answer:The probability that a randomly selected number from $S$ is odd is $\frac{1}{2}$.Hence, the correct option is C.