Practice 1Find the sample space for each of the following.
a.One coin is tossed.
b.Two coins are tossed
c.Three coins are tossed
Practice 2
a.Two coins are tossed. What is the probability that both land heads up?
b.A card is drawn from a standard deck of playing cards. What is the probabil- ity that it is an ace?
Example 3 Two six-sided dice are tossed. What is the probability that the total of the two dice is 7?
Practice 3b Twelve-sided dice,as shown in Figure 15,can be constructed (in the shape of regular dodecahedrons) so that each of the numbers from 1 to 6 appears twice on each die. Prove that these dice can be used in any game requiring ordinary six- sided dice without changing the probabilities of different outcomes.
Example 4 In a state lottery,a player chooses six different numbers from 1 to 40. If these six numbers match the six numbers drawn by the lottery commission,the player wins (or shares) the top prize. What is the probability of winning the top prize?
Practice 4b Suppose you managed a little league team. You have 8 pitchers, 10 fielders, and 5 other players on the bench. If you choose three players at random, what is the probability that they are all pitchers?
Practice 5a. One card is selected from a standard deck of 52 playing cards. What is the probability that the card is either a heart or a face card?
Practice 5b. In survey of 50 people, 21 said they owned stocks, 32 said they owned bonds and 12 said they owned both stocks and bonds. How many of the 50 people owned stocks or bonds? How many owned neither?
Example 6 The personnel department of a company has compiled data on employees’numbers of years of service. The results are shown in the table.
Years of Service Number of Employees
0–4 157
5–9 89
10–14 74
15–19 63
20–24 42
25–29 38
30–34 37
35–39 21
40–44 8
If an employee is chosen at random,what is the probability that the employee hashad nine or fewer years of service?
Practice 6b.The numbers of colleges and universities in various regions of the United States in 1996 are shown in Figure 16. One institution is selected at random. What is the probability that the institution is in one of the two north central regions? (Source:U.S.NationalCenter for Education Statistics)
Practice 7a. A random number generator on a computer selects three integers from 1 to 20.
What is the probability that all three numbers are less than or equal to 5?
Practice 7b. In 1997,58% of the population of the United States were 30 years old or older. Suppose that in a survey,ten people were chosen at random from the population. What is the probability that all ten were 30 years old or older? (Source:U.S.Bureau of the Census)
Practice 8 A manufacturer has determined that a certain machine averages one faulty unit for every 1000 it produces. What is the probability that an order of 200 units will have one or more faulty units?