NIMCET 2017 Question Paper with solutions

Let ${\mathit{E}}_1$ be the event that student knows the answer and ${\mathit{E}}_2$ be the event that student guesses the answer. Also, A be the event that he answered correctly.
Now, according to the question
P (${\mathit{E}}_1$) = 0.90 , P (${\mathit{E}}_2$) = 0.10
P $\left(\frac{\mathit{A}}{{\mathit{E}}_1}\right)$ = 1 , P $\left(\frac{\mathit{A}}{{\mathit{E}}_2}\right)$ = 0.25
Required probability
P $\left(\frac{{\mathit{E}}_2}{\mathit{A}}\right)$ = $\frac{\mathit{P}\left({\mathit{E}}_2\right)\mathit{P}\left(\frac{\mathit{A}}{{\mathit{E}}_2}\right)}{\mathit{P}\left({\mathit{E}}_1\right)\mathit{P}\left(\frac{\mathit{A}}{{\mathit{E}}_1}\right)+\mathit{P}\left({\mathit{E}}_2\right)\mathit{P}\left(\frac{\mathit{A}}{{\mathit{E}}_2}\right)}$
= $\frac{0.10\times 0.25}{0.90\times 1+0.10\times 0.25}$
= $\frac{25\times 10}{90\times 100+10\times 25}$ = $\frac{25}{900+25}$ = $\frac{1}{36+1}$ = $\frac{1}{37}$