BECE Mathematics 2024 Paper

Note1. Rolling a fair die does not influence the outcomes of tossing a fair coin2. Neither tossing a fair coin affects the outcomes of rolling a fair die3. Both events do not affect each other so they are independent events Probability $= \frac{\text{Number of possible selection}}{\text{Number of samples}}$ $P(A \cap B)=P(A) \times P(B)$Thus you calculate the probability of each event separately and multiply them to get the independent probability Samples for coin $=\{$ Head, Tail $\}$Number of samples for coin $=2$Number of tail(s) = 1$P(\text{Tail})=\frac{1}{2}$Samples for die $=\{1,2,3,4,5,6\}$Number of samples for die $=6$Odd numbers are numbers not divisible by 2 . Thus there is a remainder when divided by 2.Odd numbers from the die samples are $\{1,3,5\}$Number of odd numbers $=3$$P(\text{Odd})=\frac{3}{6}=\frac{1}{2}$Note: 3 divides itself $1$ time and 6, 2 timesP(Tail and Odd) $= P(\text{Tail}) \times P(\text{Odd})$P(Tail and Odd) $= \frac{1}{2} \times \frac{1}{2}$P(Tail and Odd) $= \frac{1 \times 1}{2 \times 2} = \frac{1}{4}$