BECE Mathematics 2024 Paper

Concept:Tossing a coin and rolling a die are independent events.So, the combined probability is the product of their separate probabilities.Solution:For the coin, the possible outcomes are Head and Tail.So, number of outcomes $= 2$.Number of favourable outcomes for Tail $= 1$.$P(\text{Tail}) = \frac{1}{2}$For the die, the possible outcomes are $\{1,2,3,4,5,6\}$.The odd numbers are $\{1,3,5\}$.Number of favourable outcomes for an odd number $= 3$.$P(\text{Odd}) = \frac{3}{6} = \frac{1}{2}$Since the events are independent:$P(\text{Tail and Odd}) = P(\text{Tail}) \times P(\text{Odd})$$P(\text{Tail and Odd}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$Answer:Option A ($\frac{1}{4}$)