1. 3% of the workers in a factory are union members. A random sample of 5 workers is taken from these workers. (a)Find the probability that the sample consists exactly 4 union members. (b)Find the probability that the sample consists of at most 2 union members. 2. A man sends 4 application forms to apply for shares in Company ABC. If the probability of each form being successful is 4/5, find the probability that he is successful in: (a) 1 application. (b) Less than 3 applications. (c) At least 3 applications. 3. 2% of the batteries produced by a factory are not satisfactory. In a sample of 12 batteries chosen at random, find the probability that: (a) Exactly 3 batteries are not satisfactory. (b) Less than 2 batteries are not satisfactory. 4. The probability of the mango chosen at random being infested by worms is 1/10. Find the expectation and standard deviation of the number of mangoes that are worm infested in a sample of 30 mangoes