Grima MAT 142
Chapter 4 Practice test PART 1
1) 200 students were asked what they expect their income to be when they graduate. 50 students
said $40,000 per year.
a) If a student is randomly selected what is the probability they predict their income will be
$40,000 per year?
b) Estimate the number of students out of 500 that would expect their income to be $40,000 per
year.
2) A TV remote control has keys for channels 0 through 9. If you select a key at random, (Write
your answers as percent’s and assume 0 is an even number)
a) What is the probability you press an even number?
b) What is the probability you press a key for odd number that is also less than 8?
3) Each individual letter of the word Tallahassee is placed on a piece of paper, and all 11 pieces
of paper are placed in a hat. If one letter is selected at random from the hat, find the probability
that: (Write your answers as a reduced fractions.)
a) the letter s is selected
b) the letter a or s is selected
4) A box contains 5 red and 4 blue marbles and 6 yellow marbles. If you select one at random
from the box, determine: (Write your answer using colons, make sure to reduce.)
a) The odds against selecting a yellow marble.
b) The odds in favor of selecting a red marble
#5-7: A card is picked from a deck of cards. Find the odds against selecting: (Write your answer
using colons, make sure to reduce.)
5) a red card 6) a black seven
7) a spade
8) A couple plans to have three children.
a) Determine the number of points in the sample space of the possible arrangements of
boys and girls.
b) Construct a tree diagram and list the sample space.
Find the probability the couple has:
c) more than 1 girl
d) A boy and 2 girls
9)
a)
b)
c)
A coin is tossed two times and a sequence of heads and tails is recorded.
Determine the number of points in the sample space.
Construct a tree diagram and list the sample space.
Find the probability that exactly one head is tossed.
#10 – 11: a single dice is rolled one time. Find the probability of rolling (Write your answer as a
reduced fraction.)
10) An odd number or a number greater than 2?
11) A number less than 3 or an even number?
#12 – 14: One card is selected from a deck of playing cards. Find the probability of selecting:
(Write your answer as a reduced fraction.)
12) A queen or a red card
13) A club or a six
14) A heart or a diamond
Answers:
1a) ¼ 1b) 125 2a) ½ 2b) 2/5 3a) 2/11 3b) 5/11 4a) 9:6 or 3:2 4b) 5:10 or 1:2
5) 26:26 or 1:1 6) 50:2 or 25:1 7) 39:13 or 3:1 8a) 8
8b) bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg 8c) ½ 8d) 3/8
9a) 4 9b) tt, th, ht, hh 9c) ½ 10) 5/6 11) 2/3 12) 7/13 13) 4/13 14) 1/2
Grima MAT 142
Chapter 4 Practice test PART 2
#15-16: Two cards are selected at random from a deck of 52 cards WITHOUT replacement.
Find the requested probabilities, (write your answer as a reduced fraction.)
15) Both cards are red
16) The first card is a 4 and the second is a 3.
#17-18: Two marbles are drawn from a bag that contains 5 blue, 3 red and 2 purple marbles
WITH replacement. Find the requested probabilities: (Write your answer as a reduced
fraction.)
17) Both are red
18) The first is not red and the second is red
#19 – 21: Create a reduced sample space and find the requested probabilities. A pair of dice is
rolled and the sum of the dice is recorded, determine the probability that: (Write your answer as
a reduced fraction.)
19) The sum is less than 3 given the second dice is a 1.
20) The sum is 4 given the first dice is a 2.
21) The sum is greater than greater than or equal to 8 given a double has been rolled.
#22 – 23: 200 1st grade students were asked if they had a cell phone. The results are given in the
table below.
Have a cell phone
Do not have a cell
phone
Total
Boys
30
60
90
Girls
35
75
110
Total
65
135
200
If one child who was in the survey is selected at random, find the probability that
22) The child selected has a cell phone, given the child is a girl.
23) The child is a boy, given they do not have a cell phone.
24) A telephone number consists of 10 digits. How many telephone numbers are possible if
neither the 1st, nor the 4th number can be a 0 or a 1? There are no other restrictions.
25) A social security number consists of nine digits. How many different social security
numbers are possible if the first three digits must be 526 and for the remaining digits repetition is
allowed?
#26-27: A license plate is to consist of two letters followed by 4 digits. How many different
codes are possible if
26) The first letter must be a vowel and the first number must be a 1 and repetition is not
permitted?
27) Repetition of numbers is NOT permitted, but repetition of letters is permitted?
28) How many ways can the letters of distinguish be arranged?
Answers:
15) 25/102 16) 4/663 17) 9/100 18) 21/100 19) 1/6 20) 1/6 21) ½
22) 35/110 = 7/22 23) 60/135 = 4/9 24) 6,400,000,000 25)1,000,000
26) 63000 27) 3,407,040 28) 604,800