Chapter 4 Review
1) A manufacturer tested 1000 Ford F250’s at random and found 15 of them to have a cosmetic
defect. If one F250 is selected at random:
a) Determine the empirical probability the truck has a cosmetic defect.
b) Estimate the number of F250’s out of 100,000 will have a cosmetic defect. (Round to the
nearest whole number)
2) A TV remote control has keys for channels 0 through 9. If you select a key at random,
a) What is the probability you do not press channel 6?
b) What is the probability you press a key for a number greater than 4??
3) Each individual letter of the word Mississippi 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 i or s is selected
4) A box contains 9 red and 2 blue marbles and 3 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 red marble.
b) The odds in favor of selecting a blue 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 heart
6) a seven
7) a black card
8) A couple plans to have two 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 a girl
9)
a)
b)
c)
A coin is tossed three 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 less than 4
11) A number less than 3 or greater than 4
#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 heart
13) A club or a four
14) A heart or a spade
#15 – 16: One marble is selected from a bag that contains 4 red, 5 white, 6 blue and 2 yellow.
Find the probability of selecting: (Write your answer as a reduced fraction.)
15) A red or a blue marble
16) A yellow or a red marble
#17-18: 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.)
17) Both cards are hearts
18) The first card is not a heart and the second card is a heart
#19-20: 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.)
19) Both are blue
20) The first is red and the second is not blue
#21 – 23: 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.)
21) The sum is greater than 10 given the second dice is a 5.
22) The sum is even given the first dice is a 2
23) The sum is greater than 4 given the first dice is a 1
#24 – 26: At a zoo, a sampling of children was asked if the zoo were to get one additional
animal, would they prefer a lion or an elephant. The results of the survey follow: (Write your
answer as a reduced fraction.)
Lion
Elephant
Total
Boys
90
110
200
Girls
75
85
160
Total
165
195
360
If one child who was in the survey is selected at random, find the probability that
24) The child selected the elephant, given the child is a girl.
25) The child is a boy, given the child preferred the lion.
26) A lock combination consists of three numbers between 0 and 30 inclusive. How many
combinations are possible, assume repetition is NOT allowed?
27) A social security number consists of nine digits. How many different social security
numbers are possible if repetition of digits is permitted?
#28-29: an identification code is to consist of two letters followed by 4 digits. How many
different codes are possible if
28) The first letter must be A, or an E and the first number must be a 1 and repetition is not
permitted?
29) Repetition of numbers is NOT permitted, but repetition of letters is permitted?
30) How many ways can the letters of peppers be arranged?
31) You plan go on a trip and want to upload a few videos to watch on the plane. You only have
storage capacity to add 8 new videos, but have 20 videos to choose from. How many
combinations videos can you choose?
32) How many groups of 3 sevens can be made from the 4 sevens in a deck of cards?
33) 4 members of a club will be selected to attend a conference. The club has 5 female and 3
male members. How many different groups can be selected if 1 male and 3 females must be
selected?
34) A class of 25 people contains 5 freshmen. If 4 people from the class are selected at random,
find the probability that none of those selected are freshmen. (Write your answer as a percent
reduced to one decimal.)
35) A committee of 6 is to be randomly selected from a group of 7 teachers and 8 students. Find
the probability the committee will consist of 3 students and 3 teachers. (Write your answer as a
percent reduced to one decimal.)
36) 2 cards are drawn from a standard deck of cards. What is the probability that 1 is a heart
and the other is black? (Write your answer as a percent reduced to one decimal.)
Answers:
1a) 15/1000 = 3/200 1b) 100,000*.015 = 1500 trucks 2a) 9/10 2b) 5/10 = 1/2
3a) 4/11 3b) 8/11 4a) 5:9 4b) 2:12 or 1:6 5) 3:1
6) 12:1 7) 1:1 8a) 4 8b) bb bg gg gb 8c) ¼ 8d) 2/4 = 1/2
9a) 8 9b) hhh hht hth htt thh tht tth ttt 9c) 3/8 = 37.5% 10) 4/6 = 2/3 11) 4/6 = 2/3
12) 16/52 = 4/13 13) 16/52 = 4/13 14) 26/52 = 1/2 15) 10/17 16) 6/17
17) 1/17 18) 13/68 19) ¼ 20) 3/20 21) 1/6 22) 3/6 = ½ 23) 3/6 = ½
24) 85/160 = 17/32 25) 90/165 = 6/11 26) 31*30*29 = 26,970 27) 1,000,000,000
28) 25,200 29) 3,407,040 30) 420 31) 125,970 32) 4 33) 30 34) 38.3% 35) 39.2%
36) 25.5%