Question 46

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waecmaths question: 

The probability of an event P happening is $\tfrac{1}{5}$ and that of event Q is $\tfrac{1}{4}$. If the event are independent, what is the probability that neither of them happens

Option A: 

$\tfrac{4}{5}$

Option B: 

$\tfrac{3}{4}$

Option C: 

$\tfrac{3}{5}$

Option D: 

$\tfrac{1}{20}$

waecmaths solution: 

$\begin{align}  & \Pr (P\cup Q)=\Pr (P)+\Pr (Q)-\Pr (P\cap Q) \\ & \Pr (P\cup Q)=\frac{1}{5}+\frac{1}{4}-\left( \frac{1}{5}\times \frac{1}{4} \right)=\frac{2}{5} \\ & \Pr (P\cup Q)'=1-\frac{2}{5}=\frac{3}{5} \\\end{align}$

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