5.12 The proportion of impurities by weight X in certain copper ore samples is a random variable having a probability density function of f (x) =.12×2(1−x),0 ≤x ≤1 0, otherwise.
If four such samples are independently selected, find the probabilities of the following events. a Exactly one sample has a proportion of impurities exceeding 0.5. b At least one sample has a proportion of impurities exceeding 0.5.