Two dice with a difference ... They appear identical, but one die is fair and the other is loaded so that the probability of throwing a 6 is 0.25. Bev picks a die at random and throws it, and it shows a 6. Find the probability that she picked the biased die.
(Hint: Let A be the event 'the die chosen is the biased one' and B be 'a die chosen at random shows a 6 when it is thrown'. Find $P(A|B).)
I know $P(A) = 1/2$, $P(B) = (1/2 \times 0.25) + (1/2 \times 1/6) = 5/24$
Don't know what $P(A|B)$ is and what to do do next.