Question 32

waecmaths question: 

In a class of 45 students, 28 students offers Chemistry and 25 offers Biology. If each students offers at least one of the two subjects. Calculate the probability that a student selected at random from the class offers Chemistry only.

Option A: 

$\tfrac{2}{9}$

Option B: 

$\tfrac{4}{9}$

Option C: 

$\tfrac{5}{9}$

Option D: 

$\tfrac{7}{9}$ 

waecmaths solution: 

$\begin{align}  & \text{Let those who offer Chemistry be }C \\ & \text{Let those who offer Biology be }B \\ & n(B)=28 \\ & n(C)=25 \\ & n(\xi )=n(B\cup C)=45 \\ & n(B\cap C)=x \\ & n(B\cup C)=n(B\cap C')+n(B'\cap C)+n(B\cap C) \\ & 45=(28-x)+(25-x)+x \\ & 45=53-x \\ & x=8 \\ & n(B\cap C)=8 \\ & \text{Those who offer Chemistry }=n(B\cap C')=28-x=28-8=20 \\ & \text{Probability of selecting those who offer Chemistry only}=\Pr (B\cap C')=\frac{20}{45}=\frac{4}{9} \\\end{align}$

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