In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are $35 \% , 20 \%$ and $10 \%$ respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is: (1) $\frac { 14 } { 45 }$ (2) $\frac { 7 } { 45 }$ (3) $\frac { 8 } { 45 }$ (4) $\frac { 28 } { 45 }$
In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are $35 \% , 20 \%$ and $10 \%$ respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is:\\
(1) $\frac { 14 } { 45 }$\\
(2) $\frac { 7 } { 45 }$\\
(3) $\frac { 8 } { 45 }$\\
(4) $\frac { 28 } { 45 }$