Question

a student either knows the answer or guesses. Let 3434 be the probability that he knows the answer and 1414 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1414 . What is the probability that the student knows the answer given that he answered it correctly?

Answer 1

Answer:
`(12)/(13)`

Explanation:

Let A = he known the answer then A' = he guess the answer.

B = he answered it correctly

As per given , we have

`P(A)=(3)/(4)\ \ ,\ \ P(A')=(1)/(4)`

`P(B|A)=1`

`P(B|A')=(1)/(4)`

By Bayes theorem , we have

`P(A|B)=(P(B|A)P(A))/(P(B|A)P(A)+P(B|A')P(A'))\\\\ P(A|B)=(1*(3)/(4))/(1*(3)/(4)+(1)/(4)*(1)/(4))\\\\= (12)/(13)`

The probability that the student knows the answer given that he answered it correctly is
`(12)/(13)` .