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Q. 4. In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $\frac{3}{4}$ be the probability that he knows the answer and $\frac{1}{4}$ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $\frac{1}{4}$ . What is the probability that the student knows the answer given that he answered it correctly?

Answers (1)

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A : Student knows answer.

B : Student guess the answer

C : Answer is correct

$P(A)=\frac{3}{4}$ $P(B)=\frac{1}{4}$

$P(C|A)=1$

$P(C|B)=\frac{1}{4}$

By Bayes theorem :

$P(A|C)=\frac{P(A).P(C|A)}{P(A).P(C|A)+P(B).P(C|B)}$

$P(A|C)=\frac{\frac{3}{4}\times 1}{\frac{3}{4}\times 1+\frac{1}{4}\times \frac{1}{4}}$

$=\frac{\frac{3}{4}}{\frac{3}{4}+\frac{1}{16}}$ $=\frac{\frac{3}{4}}{\frac{13}{16}}$

$P(A|C)=\frac{12}{13}$

Posted by

seema garhwal

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