Assignment:
Q1. If P(A) = 0.5, P(B)= 0.4, and P(B¦A) = 0.3, then P(A and B) is
Q2. If A and B are mutually exclusive events and P(A) = 0.3 and P(B) = 0.6, then P(A and B) is
Q3. How many ways can a Math Club schedule 4 speakers for 4 different meetings if they are all available on any of 6 possible dates?
Q4. A human gene carries a certain disease from mother to the child with a probability of 0.65. Suppose a mother of two children carries the gene. Also, assume that infection from child to child is independent. The probability that both children are infected with the disease is
Q5. A lot contains 20 fuses of which 5 are defective. If two fuses are selected at random without replacement, what is the probability that at most one is defective?
Q6. If A and B are two mutually exclusive events with P(A) = 0.15 and P(B) = 0.4, then P(A and B’), (i.e. probability of A and B complement) is
Q7. On a particular college campus, 65% of the non-traditional students are smokers. Research indicates that 15% of the smokers have some form of lung cancer. The probability of a non-traditional student on this campus having lung cancer given that the student is a smoker is
Q8. A large industrial firm uses three different warehouses (A, B and C) to store its manufactured product. From past records, it is known that 20% of the manufactured product are assigned to warehouse A, 50% are assigned to B, and 30% to warehouse C. If it is known that 5% of the product in warehouse A are defective, 4% in warehouse B are defective, and 8% in warehouse C are defective, what is the probability that if a product is selected at random from one of these warehouses that it will be defective?
Q9. A large industrial firm uses three different warehouses (A, B and C) to store its manufactured product. From past records, it is known that 20% of the manufactured product are assigned to warehouse A, 50% are assigned to B, and 30% to warehouse C. If it is known that 5% of the product in warehouse A are defective, 4% in warehouse B are defective, and 8% in warehouse C are defective, what is the probability that if a defective product is selected at random that it came from warehouse C?
Q10. From a group of 5 men and 6 women, how many committees of size 3 are possible with two men and 1 women if a certain man must be on the committee?
Q11. A shipment of 12 calculators contains 3 defective calculators. In how many ways can a school purchase 5 of these calculators and receive at least two of the defective calculators?
Q12. The probability that a patient recovers from an operation is 0.9. What is the probability that exactly 2 of the next 3 patients who have this operation will recover?
Provide complete and step by step solution for the question and show calculations and use formulas.