It rains in a city with a chance of 0.4. The weather forecast is not always accurate. When there will be a rain the next day, the forecast predicts the rain with probability 0.8; When there is no rain, the forecast falsely predicts a rain with probability 0.1. You take your umbrella every time rain is forecast, and you take your umbrella 25% of the times when rain is not forecast. Find the chance that it actually rains given that the forecast predicts rain. Given that it rains, what is the probability that you do not have your umbrella?
The Attempt at a Solution
Let R be the event about rain tomorrow, FR be the event about weather forecast predicts will rain tomorrow and U about I bring my umbrella.
I got the first part, P(R | FR) = P(FR | R)P(R)/(P(FR | R)P(R)+P(FR | R^c)P(R^c))
But I don't know how to do the second part.