1. 30% of pupils in a school travel to school by bus. From a sample of ten pupils chosen at random, find the probability that (a) only three travel by bus, (b) less than half travel by bus. 2. A bag contains counters of which 40% are red and rest yellow. A counter is taken from the bag, its colour noted and then replaced. This is performed eight times in all. Calculate the probability that (2) exactly three will be red, at least one will be red, more than four will be yellow Warranty records show that the probability that a new car needs a warranty repair in the first 90 days is 0.05. If a sample of three new cars is selected. Required: (a) What is the probability that none needs a warranty repair? (b) What is the probability that at least one needs a warranty repair? What is the probability that more than one needs a warranty repair? (d) What are the mean and the standard deviation of the probability distribution? The random variable X is distributed binomially with mean 2 and variance 1.6. Find (a) the probability that X is less than 6, (b) the most likely value of X