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:
$\tfrac{2}{15}$
Option B:
$\tfrac{3}{15}
Option C:
$\tfrac{7}{15}$
Option D:
$\tfrac{13}{15}$
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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