A golfer observes that, when playing a particular hole at his local course, he hits a straight drive on 80% of the occasions when the weather is not windy but only on 30% of the occasions when the weather is windy. Local records suggest that the weather is windy on 55% of all days.

(a) Show that the probability that, on a randomly chosen day, the golfer will hit a straight drive at the hole is 0.525.

(b) Given that he fails to hit a straight drive at the hole, calculate the probability that the weather is windy. (NEAB)