A) \[\frac{37}{40}\]
B) \[\frac{1}{37}\]
C) \[\frac{36}{37}\]
D) \[\frac{1}{9}\]
Correct Answer: B
Solution :
We define the following events : \[{{A}_{1}}:\] He knows the answer. \[{{A}_{2}}:\] He does not know the answer. \[E:\] He gets the correct answer. Then \[P({{A}_{1}})=\frac{9}{10},\,\,P({{A}_{2}})=1-\frac{9}{10}=\frac{1}{10},\,P\text{ }\left( \frac{E}{{{A}_{1}}} \right)=1,\] \[P\left( \frac{E}{{{A}_{2}}} \right)=\frac{1}{4}\] \[\therefore \] Required probability \[=P\left( \frac{{{A}_{2}}}{E} \right)=\frac{P({{A}_{2}})P(E/{{A}_{2}})}{P({{A}_{1}})P(E/{{A}_{1}})+P({{A}_{2}})P(E/{{A}_{2}})}=\frac{1}{37}.\]You need to login to perform this action.
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