3. The probability that it will rain is 0.3. given that it rains, the probability is 0.4 that the plane will take off on time, and given that it does not rain, the probability is 0.9 that the plane will take off on time. Find the probability that

a. It will rain and the plane will take off on time

b. It will not rain and the plane will take off on time

c. The plane will take off on time

4. The probability that a student studies is 0.7. given that he studies, the probability that he will pass a course is 0.8. given that he does not study, the probability that he will pass a course is 0.4. find the probability that

a. He will study and pass the course

b. He will not study and will pass the course

c. He will pass the course

5. Jeremy wants to buy a special ink for his printer. The probability that the university bookstore carries it is 0.4. Assuming that the two stores carries the stock item independently, find the probability that neither store carries the item

6. The probability that a plane arrives at the airport before 10AM is 0.7. The probability that a passenger leaving from a city by a bus arrive at the airport by 10AM is 0.6. find the probability that

a. The plane and the passenger arrive by 10AM

b. The plane arrives by 10AM and the passenger arrives after 10AM

7. A genetic population has two types, "A" and "a". it is known that 60% of the alleles in the population are of "A". if two alleles are picked at random, find the probability that

a. Both alleles are of "A"

b. One allele is of "A" and the other is of "a"

c. Both alleles are of "a"

8. It is known from past experience that the probability that a person has cancer is 0.02 and the probability that a person has heart disease is 0.1. If we assume that the incidence of cancer and heart disease are independent, find the probability that

a. A person has both ailments

b. A person does not have both ailments

c. A person does not have either ailment