Download Ch5 Study Questions File

STAT201 Study Questions on Chapter 5
15th ed.
Q. 19) Suppose two events A and B are mutually exclusive. What is the probability of their joint
occurence?
When two events are mutually exclusive it means that if one occurs the other event cannot
occur at the same time. Therefore, the probability of their joint occurrence is zero
Q.25) A local bank reports that 80% of its customers have a checking account, 60% have savings
account and 50% have both. If a customer is chosen at random, what is the probability the
customer has either a cheking account or a savings account? What is the probability the customer
does not have either a cheking account or a savings account?
P(C or S) = P(C) + P(S) – P(CS) = 0.80 + 0.60 – 0.50 = 0.90
P(not C and not S) = 1 – 0.90 = 0.10
Q.26) All Seanons Plumbing has two service trucks that frequently need repair. If the probability
that the first truck available is 0.75 and the the probability that the second truck available is 0.50
and both trucks is available is 0.30, what is the probability that neither truck is available?
P(A1 or A2) = P(A1) + P(A2) – P(A1 & A2) = 0.75 + 0.50 – 0.30 = 0.95
P(not A1 and not A2) = 1 – 0.95 = 0.05
Q.49) The probability the cause and the cure for all cancers will be discovered before the year
2020 is 0.20. Which approach of probability does this illustrate?
Subjective.
Q.50) A chicken factort has several stores. When interviewing applications for server positions,
the owner would like to include information on the amount of tip a server can expect to earn per
checks (bill). A study of 500 recent checks indicated that the server earned the following
amounts in tips per 8-hour shift.
Amount of Tip
$0 up to $20
20 up to 50
50 up to 100
100 up to 200
200 and more
Total
Number
200
100
75
75
50
500
a) What is the probability of a tip of $200 or more?
b) Are the categories “$0 up to $20” , “$20 up to $50” and so on considered mutually
exclusive?
c) If the probabilities associated with each outcome were totaled, what would that total be?
d) What is the probability of a tip of up to $50?
e) What is the probability of a tip of less than $200?
a.
b.
c.
d.
e.
0.10, found by 50/500
Yes, mutually exclusive, because a given tip cannot fall in more than one category.
1.00
0.60, found by 300/500
0.90, found by 450/500 or 1 – (50/500)
Q.70) An invester purchased 100 shares of Exim Bank stock and 100 shares of Santee Electric
Cooperative stock. The probability the bank stock will appreciate over a year is 70%. The
probability the electric stock will appreciate over a year is 60%.
a) What is the probability both stocks will appreciate during the period?
P(B & E) = (0.70)0.60) = 0.42
b) What is the probability the bank stock will appreciate but the electrick stock will not.
P(B & not E) = (0.70)(0.40) = 0.28
c) What is the probability at least one of the stocks appreciates?
P( at least one stock apprec.) = P(B) + P(E) – P(B&E) = 0.70 + 0.60 – 0.42 = 0.88
Some other questions:
1) An automatic machine inserts mixed vegetables into a plastic bag. Past experience
revealed that some packages were underweight and some were overweight, but most of
them had satisfactory weight.
What is the probability of selecting three packages that are satisfactory?
Answer: P(all 3 satisfactory) = (0.9) (0.9) (0.9) = 0.729
2) A study of interior designers' opinions with respect to the most desirable primary color
for executive offices showed that:
What is the probability that a designer does not prefer blue?
Answer: Total is 400. So, P(prefer Blue) = 37/400 = 0.0925
P( not prefer Blue) = 1 – P (prefer Blue) = 1 – 0.0925 = 0.9075.
3) In a survey of employee satisfaction, the following table summarizes the results in terms of
employee satisfaction and gender.
a) What is the probability that an employee is Female and Dissatisfied? Answer: 0.22
b) What is the probability that an employee is Male or Dissatisfied?
Answer: P(M or D) = P(M) + P(D) – P(M&D) = 0.60 + 0.55 – 0.33
= 0.82
c) What is the probability that an employee is Satisfied given that the employee is Male?
Answer: Total male= 27 +33 = 60 out of 100.
P(S |M) = 27/60 = 0.45
4) In a study of student preference of energy drinks, the researcher has identified a population of
10 students. To get a quick result, the researcher will select a sample of 2 students. How many
different samples are possible?
Answer: Using the combination formula ;
N
C n
10 x9 x8 x7 x6 x5 x 4 x3x 2 x1
 45
(2 x1)(8 x7 x6 x5 x 4 x3x 2 x1))
5)A lamp manufacturer has developed five lamp bases and four lampshades that could be used
together. How many different arrangements of base and shade can be offered?
Using the multiplication formula: (m)(n) = (5)(4) = 20
6) How many permutations of the two letters C and D are possible?
Answer: 2 as CD and DC