Before leaving for work, serap checks the weather report in order to decide whether to carry an umbrella. on any given day, with probability 0.2 the forecast is “rain" and with probability 0.8 the forecast is “no rain". if the forecast is “rain", the probability of actually having rain on that day is 0.8 . on the other hand, if the forecast is “no rain", the probability of actually raining is 0.1 . one day, serap missed the forecast and it rained. what is the probability that the forecast was “rain"?