waecmaths question:
If a number is selected at random from each of the sets P = {1, 2, 3} and Q ={2, 3, 5}. Find the probability that the sum of the number is prime
Option A:
$\frac{5}{9}$
Option B:
$\frac{4}{9}$
Option C:
$\frac{1}{3}$
Option D:
$\frac{2}{9}$
waecmaths solution:
$\begin{align} & \Pr (1\text{ }and\text{ }2)=\tfrac{1}{3}\times \tfrac{1}{3}=\tfrac{1}{9} \\ & \Pr (2\text{ }and\text{ }3)=\tfrac{1}{3}\times \tfrac{1}{3}=\tfrac{1}{9} \\ & \Pr (1\text{ }and\text{ }2)\text{ or }\Pr (2\text{ }and\text{ 3})=\tfrac{1}{9}+\tfrac{1}{9}=\tfrac{2}{9} \\\end{align}$
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