A population of 100 rats is tested for 4 genetic mutations after exposure to some chemicals:

mutation A, mutation B, mutation C, and mutation D. 43 rats tested positive for mutation A.

37 rats tested positive for mutation B. 37 rats tested positive for mutation C. 35 rats tested

positive for mutation D. One rat tested positive for all four mutations. 5 rats tested positive

for mutations A, B, and C. 4 rats tested positive for mutations A, B, and D. 6 rats tested

positive for mutations A, C, and D. 3 rats tested positive for mutations B, C, and D. 64 rats

tested positive for mutations A or B. 61 rats tested positive for mutations A or C. 59 rats tested

positive for mutations B or D. 58 tested positive for mutations C or D. 9 rats did not show any

evidence of genetic mutation.

(a) What is the probability that if 5 rats are selected at random, 3 will have exactly 2 genetic

mutations?

(b) What is the probability that if 4 rats are selected at random, no more than 2 will have

exactly 1 mutation?