WAEC Further Mathematics 2023 Paper

$P(X\cup Y)=\;\frac{5}{8}$

$P(X\cap Y)=P(X)\times P(Y)$

Since X and Y are independent events, the probability of their union (X ⋃ Y) can be calculated as:

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)$

$=\;\frac{5}{8}=\;\frac{1}{8}+P(Y)-\;\frac{1}{8}\times P(Y)$

$=\;\frac{5}{8}-\;\frac{1}{8}=P(Y)-\;\frac{1}{8}\times P(Y)$

$=\;\frac{1}{2}=P(Y)\left(1-\;\frac{1}{8}\right)$

$=\;\frac{1}{2}=P(Y)\left(\;\frac{7}{8}\right)$

$=P(Y)=\;\frac{1}{2}\div\;\frac{7}{8}$

$\therefore P(Y)=\;\frac{1}{2}\times\;\frac{8}{7}=\;\frac{4}{7}$