1. A pollster randomly selected 3 of 10 available people. How many different groups of three are possible?

2. A student is taking two courses, history and math. The probability the student will pass the history course is 0.57, and the probability of passing the math course is 0.74. The probability of passing both is 0.42. What is the probability of passing at least one?

3. Suppose thatP(X₁) = 0.90 andP(Y₂|X₁) = 0.40. What is the joint probability ofX₁andY₂?

4 . If you ask three strangers on campus about their birthdays, what is the probability that:(Round the final answers to 4 decimal places.)

a.All were born on Saturday?

b.All were born on different days of the week?

c.None was born on Thursday?

5 Assume that there are 24 homes in the Quail Creek area and six of them have a security system. Three homes are selected at random:

a.What is the probability all three of the selected homes have a security system?

b.What is the probability none of the three selected homes has a security system?

c.What is the probability at least one of the selected homes has a security system?

d.Did you assume the events to be dependent or independent?

6 A case of 37 cans contains one can that is contaminated. Three cans are to be chosen randomly for testing.

a.How many different combinations of three cans could be selected?

b.Of the three cans selected, what is the probability that the contaminated can is selected for testing?

7 For a weekly lottery game in Ontario, participants select three numbers between 4 and 8. A number cannot be selected more than once, so a winning ticket could be, say, 458, but not 445. Purchasing one ticket allows you to select one set of numbers. The winning numbers are announced on TV each week.

a.How many different outcomes (three-digit numbers) are possible?

b.If you purchase a ticket for the game tonight, what is the likelihood you will win?

c.Suppose you purchase three tickets for tonight's drawing and select a different number for each ticket. What is the probability that you will not win with any of the tickets?