1.(10 points) Given that P(A) = 0.42, P(B) = 0.50 and P(A and B) = 0.20, calculate the following:

a)P (A or B)

b)P (complement of the event "A or B")

c)P(A|B)

d)P(B|A)

e)Are Events A and B independent? Why?

2.(10 points) The following table shows a random sample of 100 hikers and the areas of hiking they prefer.

Gender

The coastline

Near lakes and streams

On mountain peaks

Total

Female

18

16

45

Male

14

55

Total

41

a)Complete the table.

b)Pick a random hiker. What is the probability this hiker is female and prefers the coastline?

c)Are the events "being female" and "preferring the coastline" independent events?

d)Find the probability that a person is male given that the person prefers hiking near lakes and streams.

e)Find the probability that a person is female or prefers hiking on mountain peaks.

3.(10 points) Assume the disease affects 1 of every 100,000 people and the test is very accurate. The test never generates a false negative (meaning it never misses someone who has the disease); however, roughly 1 in 10,000 tests conducted on a healthy person will generate a false positive, meaning that the person tests positive but does not have the disease. Given a positive test result, what is the probability that the person is actually healthy? (Hint: It will help you think through by drawing a tree diagram.)

4.(10 points) Approximately 70% of statistics students do their homework in time for it to be collected and graded. Each student does homework independently. In a statistics class of 20 students, what is the probability that at least 18 will do their homework on time?

5.(10 points) You notice that a news reporter says "uh," on average, two times per broadcast.

a)What is the probability that the news reporter says "uh" more than two times per broadcast?

b)Suppose the news reporter broadcasts three times a week. How many times do you expect to hear s/he says "uh" in a week?

c)What is the probability that the news reporter says "uh" more than two times in a week?