In a group of 400 people, 160 are smokers & non-vegetarian, 100 smokers & vegetarian, 140 …

Question

In a group of 400 people, 160 are smokers \& non-vegetarian, 100 smokers \& vegetarian, 140 non-smokers \& vegetarian. Chest disorder chances: 35\%, 20\%, 10\% respectively. A person with the disorder is chosen; find probability they are smoker \& non-vegetarian.

Accepted Answer

$P(A)=\dfrac25,P(B)=\dfrac14,P(C)=\dfrac{7}{20}$; $P(E\mid A)=0.35,P(E\mid B)=0.2,P(E\mid C)=0.1$.

$$P(A\mid E) = \frac{\frac25\times0.35}{\frac25\times0.35+\frac14\times0.2+\frac{7}{20}\times0.1} = \frac{14}{14+5+3.5}=\frac{28}{45}$$

Solutions · 1