Stat 101 – Sheet 8 (Solutions)
King Saud University
Almajmaa’h Engineering College
STAT 101
1430/2009
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Solution of Sheet (8)
Probability
1. Briefly explain the two properties of probability.
Answer: See page 64
2. Briefly describe an impossible event and a sure event. What is the
probability of the occurrence of each of these two events?
Answer: An event that cannot occur has zero probability; such an event is called impossible
event. An event that is certain to occur has a probability equal to 1 and is called a sure event.
That is,
For an impossible event M:
For a sure event C:
P(M) = 0
P(C) = 1
Example: suppose a box contains 5 red balls, the probability of selecting a
red ball randomly from the box is 1 and the probability of selecting one
green ball from the box is zero
3. Briefly explain the three approaches to probability. Give one example of
each approach.
Answer: the three approaches to probability are:
1) Classic probability
2) The relative frequency concept of probability, and
3) The subjective probability concept.
Examples are given in pages 65-70.
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Stat 101 – Sheet 8 (Solutions)
4. Briefly explain for what kind of experiments we use the classical approach
to calculate probabilities of events and for what kind of experiments we
use the relative frequency approach.
Answer: we use the classic approach to calculate probabilities of events
when an experiment has the same probability of occurrence (equally likely
outcomes). And we use relative frequency approach when outcomes for
the corresponding experiments are not equally likely and we can either use
past data or generate new data to calculate approximate relative
probability. If an experiment is repeated n times and an event A is observed
f times, then, according to the relative frequency concept of probability:
P(A) =
𝑓
𝑛
5. Which of the following values cannot be probabilities of events and why?
1/5 .97 −.55 1.56 5/3 0.0 −2/7 1.0
Answer: -.55 , 5/3, -2/7
6. Which of the following values cannot be probabilities of events and why?
.46 2/3 −.09 1.42 .96 9/4 −1/4 .02
Answer: -.9 , 1.42, 9/4, -1/4
7. Thirty-two persons have applied for a security guard position with a
company. Of them, 7 have previous experience in this area and 25 do not.
Suppose one applicant is selected at random. Consider the following two
events: This applicant has previous experience, and this applicant does
not have previous experience. If you are to find the probabilities of these
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Stat 101 – Sheet 8 (Solutions)
two events, would you use the classical approach or the relative
frequency approach? Explain why.
P( the applicant has previous experience) = 7/32 = 0.22
P( the applicant does not have previous experience) = 25/32 = 0.78
We use classic approach because the events are equal likely outcomes.
8. The president of a company has a hunch that there is a .80 probability
that the company will be successful in marketing a new brand of ice
cream. Is this a case of classical, relative frequency, or subjective
probability? Explain why.
It is a subjective probability, because the probability given here assigned
to an event based on subjective judgment, and experience of the
president of the company.
9. The coach of a college football team thinks there is a .75 probability that
the team will win the national championship this year. Is this a case of
classical, relative frequency, or subjective probability? Explain why.
It is a subjective probability, because the probability given here assigned
to an event based on subjective judgment, and experience of the coach
of the college football team.
10. A random sample of 2000 adults showed that 1120 of them have
shopped at least once on the Internet. What is the (approximate)
probability that a randomly selected adult has shopped on the Internet?
P (a randomly selected adult has shopped on the Internet) = 1120/2000
P = 0.56
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Stat 101 – Sheet 8 (Solutions)
11. In a group of 50 executives, 29 have a type A personality. If one executive
is selected at random from this group, what is the probability that this
executive has a type A personality?
P (executive has a type A personality) = 29/50 =0.58
12. A multiple-choice question on a test has five answers. If Dianne chooses
one answer based on “pure guess,” what is the probability that her
answer is
a. correct? = 1/5 = 0.2
b. wrong? = 4/5 = 0.8
Do these two probabilities add up to 1.0? If yes, why? Because each of
the two answers for the five questions has the same probability of being
selected.
13.Suppose you want to find the (approximate) probability that a randomly
selected family from Los Angeles earns more than $125,000 a year. How
would you find this probability? What procedure would you use? Explain
briefly.
Use relative frequency approach
You are required to explain why?
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