Question 43

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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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