Exercises. 1. The following table shows the

	B
A	0.25 0.12
	0.40

1. The following table shows the

probabilities concerning two events A and B.

a) Determine the missing entries.

b) What is the probability that A occurs and B does not occur?

c) Find the probability that either A or B occurs.

d) Find the probability that one of these events occurs and other does not.

2. A woman’s clothing store owner buys from three companies:

A, B, and C. The purchases are shown below:

Product	Company A	Company B	Company C
Dresses
Blouses

If one item is selected at random, find the following probabilities:

a) It is purchased from company A or it is a dress.

b) It was purchased from company B or company C.

c) It is a blouse or was purchased from company A.

3. In a statistics class there are 18 local and 10 foreign students: 6 of the foreign students are females, and 12 of the local students are males. If a student is selected at random, what is the probability that

a) randomly selected student is a local or a female?

b) randomly selected student is foreign or a female student?

c) randomly selected student is a local or a foreign student?

4. Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two-way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same, or worse off than their parents.

	Education level Less than Hight More than High school school high school
Better off Same Worse off	140 450 420 60 250 110 200 300 70

Suppose one adult is selected at random from these 2000 adults, find the probability that this adult is

a) financially better off his (her) parents or high school student;

b) more than high school student or financially worse off than his (her) parents;

c) financially better off his (her) parents or financially worse off his (her) parents;

d) financially better off than his (her) parents

e) financially better off than his (her) parents given that he (she) has less than high school education;

f) financially worse off than his (her) parents given that he (she) has hight school education

g) financially the same as his (her) parents given that he (she) has more than high school eduction.

h) Are the events “better off ” and ”hight school education” mutually exclusive? What about the events “less than high school” and “more than high school”? Why or why not?

i) Are the events “worse off “and “”more than high school” independent? Why or why not?

5. Eighty students in a university cafeteria were asked if they favoured a ban on smoking in the cafeteria. The results of the survey are shown in the table.

Class	Favour	Oppose	No opinion
Freshmen Sophomore

If a student is selected at random, find these probabilities:

a) He or she opposes the ban, given that the student is a freshman.

b) Given that the student favours the ban, the student is a sophomore.

6. The following table gives a two-way classification of 200 randomly selected purchases made at department store.

	Paid by cash/check Paid by credit card
Male Female	24 46 77 53

If one of these 200 purchases is selected at random, find the probability that it is

a) made by a female

b) paid by cash/check

c) paid by credit card given that the purchase is made by a male

d) made by a female given that it is paid by cash/check

e) made by a female and paid by a credit card

f) paid by cash/check or made by a male

g) Are the events “female” and “paid by credit card” independent? Are they mutually exclusive? Explain why or why not.

7. Three cable channels (6, 8, and 10) have quiz shows, comedies, and dramas. The table gives proportions in the nine joint classifications

Channels   Type of show	Channel 6 Channel 8 Channel 10
Quiz show Comedy Drama	0.21 0.11 0.06 0.08 0.21 0.08 0.01 0.07 0.17

a) What proportion of shows is quiz show?

b) What proportion of shows does Channel 6 have?

c) If randomly selected show is quiz show, what is the probability that it was shown on channel 6?

d) If the show was shown on channel 10, what is the probability that it was comedy?

e) What is the probability that randomly chosen show is drama, or shown on channel 8, or both?

8. A supermarket manager classified customers according to whether their visits to the store as frequent or infrequent and whether they often, sometimes, or never make a purchase. The accompanying table gives the proportions of people surveyed in each of six joint classifications:

Making purchase   Frequency of visit	Often Sometimes Never
Frequent Infrequent	0.12 0.48 0.19 0.07 0.06 0.08

a) What is the probability that a customer is both a frequent shopper and often purchases?

b) What is the probability that a customer who never makes purchase visits the store frequently?

c) Are the events “Never makes a purchase” and “Visits the store frequently” independent?

d) What is the probability that a customer who infrequently visits the store often makes a purchase?

e) Are the events “Often makes a purchase” and “Visits the store infrequently” independent?

f) What is the probability that a customer frequently visits the store?

g) What is the probability that customer never makes a purchase in this store?

h) What is the probability that a customer either frequently visits the store or never makes a purchase, or both?

9. The accompanying table shows proportions of salespeople classified according to marital status and whether or not they own stocks.

Own stocks Martial status	Yes No
Married Single	0.64 0.13 0.17 0.06

a) What is the probability that a randomly chosen salesperson was married?

b) What is the probability that a randomly chosen salesperson does not own stocks?

c) What is the probability that randomly chosen single salesperson does not own stocks?

d) What is the probability that a randomly chosen salesperson who owns stocks was married?

10. Forty-two percent of employees in a large corporation were in favour of a modified health care plan, and 22% of the corporation employees favoured a proposal to change the work schedule. Thirty- four percent of those favouring the health plan modification favoured the work schedule change.

a) What is the probability that a randomly selected employee is in favour of both modified health care plan and the changed work schedule?

b) What is the probability that a randomly chosen employee is in favour of at least one of these two changes?

c) What is the probability that a randomly selected employee favouring the work schedule change also favours the modified health plan?

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