(a) In a school, the ratio of those who passed to those who failed in a History test is 4 : 1. If 7 students are selected at random from the school, find, c...

(a) In a school, the ratio of those who passed to those who failed in a History test is 4 : 1. If 7 students are selected at random from the school, find, correct to two decimal places, the probability that :

(i) at least 3 passed the test ; (ii) between 3 and 6 students failed the test.

(b) A fair die is thrown five times; find the probability of obtaining a six three times.