A) \[\frac{8}{17}\]
B) \[\frac{9}{17}\]
C) \[\frac{11}{17}\]
D) \[\frac{6}{17}\]
Correct Answer: B
Solution :
let A denote the event of correct diagnosis and E the event of patients death. It is given that |
\[P(A)=\frac{60}{100},P(\overline{A})=\frac{40}{100}\] |
\[P(E/A)=\frac{75}{100}\] and \[P\left( \frac{E}{\overline{A}} \right)=\frac{80}{100}\] |
By Bayes? theorem |
\[P\left( \frac{A}{E} \right)=\frac{P(A)P(E/A)}{P(A)P(E/A)+P(\overline{A})P(E/\overline{A})}\]\[=\frac{\frac{60}{100}+\frac{75}{100}}{\frac{60}{100}\times \frac{75}{100}+\frac{40}{100}\times \frac{80}{100}}\] |
\[=\frac{\frac{3}{5}\times \frac{3}{4}}{\frac{3}{5}\times \frac{3}{4}+\frac{2}{5}\times \frac{4}{5}}=\frac{9}{17}\] |
You need to login to perform this action.
You will be redirected in
3 sec