Maths --- hard Probability question

Let
K:She knows the correct answer
N:She don't know the correct answer
T:Her answer is correct
F:Her answer is wrong
Then
P(K)=0.5,P(N)=0.5
P(T|K)=1,P(T|N)=0.2
P(T)=P(K)*P(T|K)+P(N)*P(T|N)=0.5+0.5*0.2=0.6
P(K|T)=P(K)P(T|K)/P(T)=0.5/0.6=5/6
The conditional probability that the student knew the answer to a question given that she answered it correctly is 5/6
(b)
From part (a)
The probability that the student answerrd a question correctly is equal to P(T)=0.6

2007-10-04 01:38:07 補充：
P(K|T)=P(K)P(T|K)/P(T) using Bayes theorem