Probability...........

The probability that a train is at least 5 minutes late is 0.5 and the probability that it is less than 10 minutes late is 0.8. What is the probability that it is going to be less than 10 minutes late, given that we know it is going to be at least 5 minutes late?

P(< 5 mins late & < 10 mins late) = 0.5*1 = 0.5
P(≥ 5 mins late & < 10 mins late) = 0.5x
P(< 10mins late) = 0.5(1+x) = 0.8 => x = 0.6

P(< 10 mins late | ≥ 5mins late) = 0.5x/0.5(1+x) = 3/8 <------