Three messenger services deliver to a small town in Oregon. ServiceAhas 60% of all the scheduled deliveries, serviceBhas 30%, and serviceChas the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively.

a. What proportion of the packages in the town are delivered on time?

b. A package arrived on time.What is the probability it was delivered by service B?

c. A package arrived on time.What is the probability it was delivered by service A?

d. You give your package to service C.What is the probability it'll be delivered late?

e.What proportion ofthe packages in the town are delivered late?

If P(A) = 0.34 and P(A or B)=0.61 and P(A and B) = 0.12, then P(B) =

A government agency has 6,000 employees. The employees were asked whether they preferred a four-day work week (10 hours per day), a five-day work week (8 hours per day), or flexible hours. You are given information on the employees' responses broken down by gender.

Male

Female

Total

Four days

300

600

900

Five days

1,200

1,500

2,700

Flexible

300

2,100

2,400

Total

1,800

4,200

6,000

a.

What is the probability that a randomly selected employee is a man and is in favor of a four-day work week?

b.

What is the probability that a randomly selected employee is female?

c.

A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours.

d.

What percentage of employees is in favor of a five-day work week?

e.

Given that a person is in favor of flexible time, what is the probability that the person is female?

f.

What percentage of employees is male and in favor of a five-day work week?

If A and B are independent evens with P(A) = 0.33 and P(B) = 0.44, then P(A Given B) =

If A and B are independent evens with P(A) = 0.43 and P(B) = 0.43, then P(A and B) =

If A and B are mutually exclusive events with P(A) = 0.32 and P(B) = 0.26, then P(A Given B) =

If P(A) = 0.33 and P(B)=0.42 and P(A and B) = 0.23, then P(A or B) =

If P(A) = 0.39,P(B)= 0.46, andP(A and B) =0.14, then P(A given B) =

Two events A and B are mutually exclusive.If P(A) = 0.21 and P(B)= 0.36, then P(A or B) =

If P(A) = 0.26, P(B) = 0.28, and P(A U B) = 0.49, then P(A | B) =

You pull two cards from a deck of cards.What is the probability that they both are Queens?

What is P( 2 of Hearts | Number cards)?Note:Ace is considered to be a number card. 2 of Hearts means pulling a 2 which is also a Hearts.

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.

underweight 2.5%

satisfactory 90%

overweight 7.5%

What is the probability of selecting three packages that are overweight?

In a finance class, the final grade is based on three tests. Historically, the instructor tells the class that the joint probability of scoring "A"'s on the first two tests is 0.5. A student assigns a probability of 0.9 that she will get an "A" on the first test. What is the probability that the student will score an "A" on the second test given that she scored an "A" on the first test?