Chapter 3 Extra Review
Name ______________________
1. Shipment of 30 calculators contains six defective units. In how many ways can a school
buy ten of these units and receive:
a)
b)
c)
d)
No defective units
One defective unit
At least nine good units?
What is the probability of the school buying five defective units?
2. In any given season, a soccer team plays 65% of their games at home. When the team
plays at home, they win 83% of their games. When they play away from home, they win
26% of their games. If the team does not win the game, find the probability that the
game was played at home.
3.
Bag A contains 5 brown and 4 black balls. Bag B contains 3 brown and 6 black balls. A
die with 5 faces marked ‘A’ and 1 face marked ‘B’ is rolled and used to select bag A or B.
A ball is then selected from this bag. Determine the probability that the ball was chosen
from A given it is black.
4.
In a Statistics class of 33 students, 17 students are involved in a club and 21 students
are in a sport and one does neither. How many students are involved in both a club and
a sport?
5.
6. A simple random sample of adults living in a suburb of a large city was selected. The
age and annual income of each adult in the sample were recorded. The resulting data
are summarized in the table below.
Age Category
21-30
31-45
46-60
Over 60
Total
$25,000$35,000
8
22
12
5
47
Annual Income
$35,000Over $50,000
$50,000
15
27
32
35
14
27
3
7
64
96
Total
50
89
53
15
207
a) What is the probability that a person chosen at random from those in this sample will be
in the 31-45 age category?
b) What is the probability that a person chosen at random from those in this sample whose
incomes are over $50,000 will be in the 31-45 age category? Show your work.
c) Based on your answers to a) and b), is annual income independent of age for those in
this sample? Explain.
Chapter 3 Extra Review
Name ______________________
Answers
1.
(Def)(Not Def)
a) (no defective) = 6 C0  24 C10  1,961,256
b) (one defective) =
6
C1 24 C9  7,845,024
c) (at least nine good) =
d) P(five defective) =
6
6
C1  24 C9  6 C0  24 C10  9,806,280
C5  24 C5
 0.00849
C
30 10
2.
89
3. a. P( 31- 45 age category) = 207 = 0.42995 ≈ 43%
35
b. 𝑃 (31 − 45 𝑎𝑔𝑒|50,000 + 𝑖𝑛𝑐𝑜𝑚𝑒 ) = 96 = 0.365 ≈ 37%
c. If they are independent then 𝑃 (31 − 45 𝑎𝑔𝑒|50,000 + 𝑖𝑛𝑐𝑜𝑚𝑒 ) = P(31 – 45); But they are
not equal so they are NOT independent.