The percentage of people given an antirheumatoid medication who suffer severe, moderate, or minor side effects are 10, 20, and 70%, respectively. Assume that people react independently and that 20 people are given the medication.

Determine the following:

(a) The probability that 2, 4, and 14 people will suffer severe, moderate, or minor side effects, respectively

(b) The probability that no one will suffer severe side effects

(c) The mean and variance of the number of people that will suffer severe side effects

(d) What is the conditional probability distribution of the number of people who suffer severe side effects given that 19 suffer minor side effects?

(e) What is the conditional mean of the number of people who suffer severe side effects given that 19 suffer minor side effects?