Download Math 2 Unit 6 Probability Review Problems

Math 2 Unit 6 Probability Review Problems
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Problem Set 1:
A security company has developed a lie detector that analyzes the stress in a person’s voice to
determine whether the person is telling the truth. The company claims the device to be accurate
94.7% of the time.
1. Suppose that this device is applied to a panel of candidates running for political office. If
the claim is true, what is the probability that the device is correct in analyzing the truth of
one candidate’s statements?
2. Suppose 4 candidates are on the panel. What is the probability that the device can
correctly analyze the integrity of all of the candidates’ statements?
3. What is the probability that the device is not able to correctly judge all four candidates’
statements?
Problem Set 2:
US telephone numbers consist of a 3-digit area code, a 3-digit exchange, and a 4-digit station
number.
1. In how many ways can you arrange the 3-digit exchange and 4-digit station number to
form a telephone number?
2. Suppose that someone randomly dials the area code in a long distance call (in the US).
The exchange and station numbers match yours. What is the probability that the number
dialed is your phone number? (note: even though some area codes are not valid, such as
000, it is still possible to dial these numbers).
Problem Set 3:
Your company orders a large shipment of scientific calculators from an office supply store.
Since the supply house does not have enough of any one brand, it substitutes other brands with
similar functions. The packing list reports this distribution of brands.
1. If all the calculators are randomly distributed to the company staff, what is the probability
that you will receive a Brand A calculator?
2. Still assuming random distribution of the calculators to the company staff, identify the
possible outcomes of such a handout of calculators. Are the possible outcomes resulting
from this random distribution of calculators mutually exclusive?
3. Suppose you decide that the Brand B calculator is of equal quality as Brand A. You will
be satisfied if you received either. What is the probability that you will receive either
Brand A or Brand B?
Problem Set 4:
The school cafeteria offers the following options for its sandwiches:
Bread:
White, Wheat
Meat:
Turkey, Ham, Bologna
Cheese:
Cheddar, American, Swiss
Spread:
Mayonnaise, Mustard
Topping:
Tomato, Lettuce, Onion
1. Suppose that one item from each of the five categories to make a sandwich. How many
different kinds of sandwiches are possible?
2. Suppose a sandwich is chosen at random from all the possible sandwiches. What is the
probability that the sandwich is turkey, on wheat bread, with American cheese, mayo,
and tomato?
3. What is the probability that a sandwich that is randomly selected from all of the possible
sandwiches will not be on white bread?
4. What is the probability that a sandwich that is randomly selected from all the possible
sandwiches will not have bologna, American cheese or tomato?
Problem Set 5:
You inspect the trees in your orchard for a certain parasite that has appeared in some of your
trees. You collect samples from 30 randomly selected trees. Your analysis shows that 12 of the
samples are infested and the rest are clean.
1. What are the two possible events that can occur in your orchard trees with respect to the
parasitic infestation?
2. Are these events mutually exclusive?
3. Are these events equally likely?
4. What is the probability that a randomly selected tree from your orchard is infested with
this parasite?
Problem Set 6:
Your company is going to have an open house. A three-member committee is needed to plan the
activities. Since all of the workers in your office want to be on the committee, a drawing will be
held to elect members. Three names will be selected randomly from a hat containing the names
of the seven workers in your office. The first name drawn will be the chairperson of the
committee, the second will act as secretary, and the last will be the treasurer.
1. How many different ways are there to construct this committee?
2. Is each of these arrangements of three workers mutually exclusive?
3. Are these events equally likely?
4. What is the probability that you will be selected to be the chairperson of the committee?
Problem Set 7:
A person’s blood is one of four possible types, A, B, AB or O, depending on the person’s gene
pair. The gene pair is the result of the combination of the gene pairs from the person’s parents.
Type A, for example, results from the combination yielding gene pairs of AA.
1. Create a chart of possible outcomes of gene pairs for a parent with AA and another of AB
genes.
2. List the probabilities for each of the possible gene pairs.
3. Out of a population of 100 children whose parents have the gene pairs above,
approximately how many would you expect to have blood type A? AB? B?
Problem Set 8:
There are three major manufacturing companies that make a product: Aberations, Brochmailians,
and Chompielians. Aberations has a 50% market share, and Brochmailians has a 30% market
share. 5% of Aberations' product is defective, 7% of Brochmailians' product is defective, and
10% of Chompieliens' product is defective.
1. What is the probability that a randomly selected product is defective?
2. What is the probability that a defective product came from Brochmailians?