EC 233 - PS 2
1) (Textbook 2.66) Suppose that the number of distributors is M = 10 and that there are n =7 orders to be placed.
a) What is the probability that all of the orders go to different distributors?
b) Distributor I gets exactly two orders and Distributor II gets exactly three orders
c) Distributors I, II and III get exactly two, three and one order(s) respectively? The remaining unassigned order can be assigned to the remaining distributors.
2) (Textbook 2.71) If two events, A and B, are such that P(A) = 0.5 and P (B) = 0.3 and
P (A∩B) = 0.1, find the following:
a. P(A|B) = b. P(B|A) = .
c. P(A| BA∪ ) = d. P(A|A∩B) =
e. P(A∩B| BA∪ ) =
3) (Textbook 2.90) Suppose that there is a 1 in 50 chance of injury on a single skydiving attempt.
a) If we assume that the outcome of different jumps are independent, what is the probability that a skydiver is injured twice?
b) A friend claims then there is a 100% chance of injury if a skydiver jumps 50 times. Is your friend correct? Why?
4) (Textbook 2.91) Can A and B be mutually exclusive if P(A) = 0.4 and P(B) =0.7? Why?
5) The probability of surviving a certain transplant operation is 0.55. If a patient survives the operation, the probability that his or her body will reject transplant within a month is 0.20. What is the probability of surviving both of these critical stages?
(On Bayes’ Theorem )
6) In a certain community 8% of all adults over 50 years of age have diabetes. Suppose that a health service in this community correctly diagnoses 95% of all persons with diabetes as having the disease. It also incorrectly diagnoses 2% of all persons without diabetes as having the disease. A person over the 50 years of age is selected at random from this community.
a) Find the probability that the community health service will diagnose this person as having diabetes
b) Given that this person is diagnosed by the health service as having the diabetes, what is the probability that he really has diabetes ?
7) (Textbook 2.124) A population of voters contains 40% Republicans and 60% Democrats. It is reported thta 30% of the Republicans and 70% of the Democrats favor an election issue. A person chosen at random from this population is found to favor the issue in question. Find the conditional probability that this person is democrat.
8) Tell whether each of the following is a discrete or a continuous random variable.
a) The number of beers sold at a bar during a particular week.
b) The length of time it takes a person to drive 50 miles.
a) The interest rate on 3-month Treasury bills
b) The number of products returned to a store on a particular day.