Answer:
The probability that he knows the answer given his answer is correct is 0.8571
Step-by-step explanation:
The problem can be solved by Bayes theorem
Let us take the Following Events
1) P(A)= probability that the student's answer is correct
2) P(B) = probability that the student knows the correct answer
For 2 events A and B Bayes theorem states that
The probability that an event 'B' occurs provided that event A has already occurred is given by "P(B|A)" as
[tex]P(B|A)=\frac{P(A|B)\cdot P(B)}{P(A)}[/tex]
where
P(A|B) is the probability of event A to occur provided event B has occurred
from the given data we have
P(B) = 0.6
P(A) (probability that his answer is correct = probability that his answer is correct provided he knows the answer + Probability his answer is correct provided he gambles)
Thus
[tex]P(A)=1\times 0.6+\frac{1}{4}\times 0.4=0.7[/tex]
Thus
[tex]P(B|A)=\frac{1\times 0.6}{0.7}=0.8571[/tex]
