1
Chapter 4:
1. How many five-digit zip codes are possible?
(a) if digits can be repeated. (b) if there cannot be repetitions.
2. Pine Pizza Palace sells pizza plain or with one or more of the following toppings:
pepperoni, sausage, mushroom, olives, onions, or anchovies. How many different
pizzas can be made?
3. Use a tree diagram to list all possible outcome for the gender of three children in a
family.
4. How many ways can 3 cars and 4 trucks be selected from 8 cars and 11 trucks to
be tested for a safety inspection?
5. If a woman can select one of three nail-polish colors, one of five lipstick shades,
and one of four blush shades, how many different combinations can she make?
6. A die is rolled one time, find the probability of
(a) getting an odd number.
(b) getting a number less than 7.
(c) Getting a number greater than 2 or an odd number.
7. Two dice are rolled one time, find the probability of
(a) getting a sum of 8.
(b) getting a sum less than or equal to 4.
(c) getting doubles.
(d) getting a sum of 7 or 11.
8. If one card is drawn from a deck of 52 playing cards. Find the probability of
(a) getting a 4 or a spade.
(b) getting a heart or a club.
(c) getting a black card or a 10.
9. A local postal carrier distributes first-class letters, advertisements, or magazines.
For a certain day, she distributed the following number of each type of item.
Delivered to 1-st class letters Ads Magazines
Home
325
406 203
Business
732
1021 97
If an item of mail is selected at random, find the probability that
(a) the item went to a home.
(b) The item was an ad or it went to a business.
(c) The item was a first-class letter or it went to a home.
2
10. The following distribution represents the length of time a patient spends in a
hospital.
Days
0-3
4-7
8-11
12-15
16+
Frequency
2
15
8
6
9
If a patient is selected, find the probability that
(a) the patient spends 3 days or less in the hospital.
(b) The patient spends less than 8 days in the hospital.
(c) The patient spends 16 or more days in the hospital.
(d) The patient spends a maximum of 11 days in the hospital.
11. A flashlight has six batteries, two of which are defectives. If two batteries are
selected at random without replacement,
(a) find the probability that both are defective.
(b) Find the probability that the first battery tests good and the second one is
defective.
12. A manufacturer has three factories, A, B, and C. They produce 50%, 30%, and
20%, respectively, of specific model of car. Thirty percent of the cars produced
in factory A are white, 40% of those produced in factory B are white, and 25%
produced in factory C are white. If an automobile produced by the company is
selected at random, find the probability that it is white.
13. A circuit to run a model railroad has eight switches. Two are defective. If a
person selects two switches at random and tests them, find the probability that the
second is defective, given that the first one is defective.
14. In a pizza restaurant, 95% of the customers order pizza. If 63% of the customers
order pizza and a salad, find the probability that a customer who orders pizza will
also order a salad.
15. In a large shopping mall, a marketing agency conducted a survey on credit cards.
The results are shown in the table.
Employment Owns a credit card Does not own a credit card
Employed
18
30
Unemployed 27
35
If a person is selected at random, find the probability that
(a) the person owns a credit card, given that the person is employed.
(b) The person is unemployed, given that the person does not own a credit card.
3
16. If a family has 5 children, find the probability that at least one boy.
17. It has been found that 6% of all automobiles on the road have defective brakes. If
five automobiles are stopped and checked by the state police, find the probability
that at least one will have defective brakes.
ANSWERS : ( If you obtain a different answer, please let me know.)
1
Answer
100000, 30240
2
Answer
64
4
7
10
13
16
18480
5/36, 1/6, 1/6, 2/9
1/20,17/40,9/40,5/8
1/7
31/32
5
8
11
14
17
60
4/13, ½, 7/13
1/15, 4/15
63/95
0.266
3
6
9
12
15
Answer
BBB,BBG,GBB,BGB,BGG,
GBG,GGB,GGG
½, 1, 5/6
467/1392, 47/58, 833/1392
0.32
3/8, 7/13