Question

In answering a question on a multiple choice test, a student either knows the answer or guesses, Let $\frac{3}{5}$ be the
Probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses.
Assuming that a student whop guesses at the answer will be correct with
probability $\frac{1}{3}$, what is the probability that
the student knows the answer given that he answered it correctly?

Answer 1

The student has to answer correctly.

Case i:-

He knows the answer.

$P\left(A\right)=\frac{3}{5}$

Case ii:-

He guesses the answer $P\left(B\right)=\frac{2}{5}$

for the guess to be correct $P\left(C\right)=\frac{1}{3}$

P(Total)$=$case i$+$ case-ii

$=P\left(A\right)+P(B\cap C)$

$=P\left(A\right)+P\left(B\right)\times P\left(C\right)=\frac{3}{5}+\frac{2}{3}\times \frac{1}{3}$

$=\frac{11}{15}$.