Question 50

Jambmaths question: 

The probabilities that a man and his wife live for 80 years are $\tfrac{2}{3}$and $\tfrac{3}{5}$respectively. Find the probability that at least one of them will live up to 80 years

Option A: 


Option B: 


Option C: 


Option D: 


Jamb Maths Solution: 

$\begin{align}  & Prob(M)=\tfrac{2}{3} \\ & Prob({{M}^{1}})=1-\tfrac{2}{3}=\tfrac{1}{3} \\ & Prob(W)=\tfrac{3}{5} \\ & Prob({{W}^{1}})=1-\tfrac{3}{5}=\tfrac{2}{5} \\ & Prob(M\cup W)=Prob(M\cap {{W}^{1}})+Prob({{M}^{1}}\cap W)+Prob(M\cap W) \\ & Prob(M\cup W)=(\tfrac{2}{3}\times \tfrac{2}{5})+(\tfrac{1}{3}\times \tfrac{3}{5})+(\tfrac{2}{3}\times \tfrac{3}{5}) \\ & Prob(M\cup W)=\tfrac{4}{15}+\tfrac{3}{15}+\tfrac{6}{15} \\ & Prob(M\cup W)=\tfrac{13}{15} \\\end{align}$

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