Chapter 4 Practice Problems
1) If two dice are rolled one time, find the probability of getting these results.
a) A sum of 6.
Before we start, let’s find the sample space
If you roll two dice, the
Sample Space is {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),
(2,1),(2,2),(2,3),(2,4),(2,5), (2,6),
…………………………………..
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}  36 possibilities
(1,2) means one die landed on 1 and the other die landed on 2.
Those who have the sum of 6 are {(1,5),(5,1),(2,4),(4,2),(3,3)}  That’s 5
5
P(a sum of 6)=
36
b) A sum of 7 or 11.
d) A sum greater than 4.
2) At a convention there are 7 mathematics instructors, 5 computer science instructors, 3
statistics instructors, and 4 science instructors. If an instructor is selected, find the probability of
getting a science instructor or a math instructor.
3) Selecting a Student In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors
are females, and 12 of the juniors are males. If a student is selected at random, find the
probability of selecting the following.
Male
Female
Total
Senior
4
6
10
Junior
12
6
18
Total
16
12
28
a.
P(A junior or a female) = (18/28) + (12/28)-(6/28) = 24/28 = 6/7
b. P(A senior or a female) = (10/28) + (12/28) –(6/28) = 16/28= 4/7
4) Games Sixty-nine percent of U.S. heads of households play video or computer games.
Choose 4 heads of households at random. Find the probability that
a. P(None play video or computer games)= (0.31)4 = 0.009 or 0.9%
b. P(all four play video or computer games)=(0.69)4 = 0.227 or 22.7%
5) If 2 cards are selected from a standard deck of 52 cards without replacement, find these
probabilities.
a. P (Both are spades) =P (1st is a spade) * P (2nd is a spade) = (13/52)*(12/51) = (1/17)
b. P (Both are the same suit) = P (1st is a suit) * P (2nd is a suit) = (4/4)* (12/51) =12/51=4/17
c. P (Both are kings) = P (1st king) *P (2nd king) = (4/52)*(3/51) = 1/221
6) In a scientific study there are 8 guinea pigs, 5 of which are pregnant. If 3 are selected at
random without replacement, find the probability that all are pregnant.
7) In a civic organization, there are 38 members; 15 are men and 23 are women. If 3 members
are selected to plan the July 4th parade, find the probability that all 3 are women. Would you
consider this event likely or unlikely to occur? Explain your answer.
P(1st is a woman)*P(2nd is a woman)*P(3rd is a woman)= (23/38)(22/37)(21/36) = 0.2100
Since the probability of getting all 3 women is small, the event is unlikely to occur.
8) Below are listed the numbers of doctors in various specialties by gender.
Pathology
Pediatrics
Psychiatry
Total
Male
12,575
33,020
27,803
73,398
Female
5,604
33,351
12,292
51,247
Total
18,179
66,371
40,095
124,645
Choose 1 doctor at random.
33,020
P(male and pediatrician) 124,645 33,020
a. P(male | pediatrician) =


 0.498
66,371
P(pediatrician)
66,371
124,645
5,604
P(pathologist and female) 124,645 5,604

 0.109
b. P(pathologist | female) =
51,247
P(female)
51,247
124,645
32) How many different ways can 7 different video game cartridges be arranged on a shelf?
7!=5040
9) How many different 3-digit identification tags can be made if the digits can be used more than
once? If the first digit must be a 5 and repetitions are not permitted?
b)
1 9  8  72
10) There are 22 threatened species of reptiles in the United States. In how many ways can you
choose 4 to write about?
(Order is not important.)
22
C4  7315
11) How many different 4-letter permutations can be formed from the letters in the word
decagon?
Similar to a problem done in class
7
P4  840
12) A parent-teacher committee consisting of 5 people is to be formed from 25 parents and 6
teachers. Find the probability that the committee will consist of these people. (Assume that the
selection will be random.)  similar to #2 p. 248 and #6 P. 249
C5
31 C5
b. 2 teachers and 3 parents
a. All teachers
c. All parents
6
C5
31 C5
25