Statistics for Business and Economics Ch4
If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪ B) = 0.88, then P(B A) =
0.04
Assume you have applied for two jobs A and B. The probability that you get an offer for job A is 0.23. The probability of being offered job B is 0.19. The probability of getting at least one of the jobs is 0.38. a. What is the probability that you will be offered both jobs? b. Are events A and B mutually exclusive? Why or why not? Explain.
0.04, No, because P(A ∩ B) ≠ 0
If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A B) =
0.05
An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is
0.100
If a coin is tossed three times, the likelihood of obtaining three heads in a row is
0.125
If P(A) = 0.48, P(A ∪ B) = 0.82, and P(B) = 0.54, then P(A ∩ B) =
0.2000
If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88, then P(A ∩ B) =
0.2100
If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩ B) =
0.24
If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A B) =
0.38
If P(A) = 0.45, P(B) = 0.55, and P(A ∪ B) = 0.78, then P(A B) =
0.40
If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =
0.400
If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =
0.43
If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A ∪ B) =
0.48
Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is
0.50
If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A ∪ B) =
0.55
If P(A) = 0.68, P(A ∪ B) = 0.91, and P(A ∩ B) = 0.35, then P(B) =
0.58
If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A ∪ B) =
0.68
Given that event E has a probability of 0.31, the probability of the complement of event E
0.69
If P(A) = 0.58, P(B) = 0.44, and P(A ∩ B) = 0.25, then P(A ∪ B) =
0.77
Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. Then, P(Bc) =
0.8
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∪ B) =
0.8
An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is
24
Assume your favorite soccer team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist?
27
Some of the CDs produced by a manufacturer are defective. From the production line, 5 CDs are selected and inspected. How many sample points exist in this experiment?
32
A college plans to interview 8 students for possible offer of graduate assistantships. The college has three assistantships available. How many groups of three can the college select?
56
An experiment consists of selecting a student body president, vice president, and a treasurer. All undergraduate students, freshmen through seniors, are eligible for the offices. How many sample points (possible outcomes as to the classifications) exist?
64
Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment?
64
37. Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 3 customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is
8
Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female. The number of sample points in this experiment is
8
Assume your favorite soccwr team has 2 games left to finish the season. The outcome of each game can be win, lose or tie. The number of possible outcomes is
9
Ten individuals are candidates for positions of president, vice president of an organization. How many possibilities of selections exist?
90
The union of events A and B is the event containing all the sample points belonging to
A or B or both
The probability assigned to each experimental outcome must be
between zero and one
In an experiment, events A and B are mutually exclusive. If P(A) = 0.6, then the probability of B
cannot be larger than 0.4
A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the
classical method
When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the
classical method
One of the basic requirements of probability is
if there are k experimental outcomes, then ∑P(Ei) = 1
Two events are mutually exclusive
if they have no sample points in common
If P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.30, then events A and B are
independent events
A sample point refers to the
individual outcome of an experiment
The symbol ∩ shows the
intersection of two events
The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A
may occur
The intersection of two mutually exclusive events
must always be equal to 0
If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are
mutually exclusive
Events that have no sample points in common are
mutually exclusive events
Initial estimates of the probabilities of events are known as
prior probabilities
A method of assigning probabilities based on historical data is called the
relative frequency method
When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the
relative frequency method
A method of assigning probabilities based upon judgment is referred to as the
subjective method
The multiplication law is potentially helpful when we are interested in computing the probability of
the intersection of two events
Bayes' theorem is used to compute
the posterior probabilities
The collection of all possible sample points in an experiment is
the sample space
The set of all possible outcomes of an experiment is
the sample space
The set of all possible sample points (experimental outcomes) is called
the sample space
The sample space refers to
the set of all possible experimental outcomes
The symbol ∪ shows the
union of events
The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called
Combination
a sample point
Each individual outcome of an experiment is called
1/2
If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is
In statistical experiments, each time the experiment is repeated
a different outcome may occur
A graphical method of representing the sample points of an experiment is
a tree diagram
Any process that generates well-defined outcomes is
an experiment
On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and "cold" weather is .15. Are snow and "cold" weather independent events?
yes
Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is
zero
The range of probability is
zero to one
If two events are mutually exclusive, then their intersection
will be equal to zero
If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X Y) =
0.0000
From nine cards numbered 1 through 9, two cards are drawn. Consider the selection and classification of the cards as odd or even as an experiment. How many sample points are there for this experiment?
4
From among 8 students how many committees consisting of 3 students can be selected?
56
A graphical device used for enumerating sample points in a multiple-step experiment is a
None of these alternatives is correct.
A perfectly balanced coin is tossed 6 times, and tails appears on all six tosses. Then, on the seventh trial
None of these alternatives is correct.
If P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)
None of these alternatives is correct.
If two events are independent, then
None of these alternatives is correct.
Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is
None of these alternatives is correct.
The union of two events with nonzero probabilities
None of these alternatives is correct.
Events A and B are mutually exclusive. Which of the following statements is also true?
P(A ∪ B) = P(A) + P(B)
Which of the following statements is always true?
P(A) = 1 - P(Ac)
The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called
Permutation
The addition law is potentially helpful when we are interested in computing the probability of
the union of two events
Two events with nonzero probabilities
can not be both mutually exclusive and independent
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∩ B) =
0.00
Events A and B are mutually exclusive if their joint probability is
0
A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is
1,000
The sum of the probabilities of two complementary events is
1.0
If a dime is tossed four times and comes up tails all four times, the probability of heads on the fifth trial is
1/2
If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is
1/2
A six-sided die is tossed 3 times. The probability of observing three ones in a row is
1/216
If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is
1/36
If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is
1/6
Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are possible?
10
A student has to take 9 more courses before he can graduate. If none of the courses are prerequisite to others, how many groups of four courses can he select for the next semester?
126
From a group of six people, two individuals are to be selected at random. How many possible selections are possible?
15
An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?
16
An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is
16
Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)
16
Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?
2/52
From a group of seven finalists to a contest, three individuals are to be selected for the first and second and third places. Determine the number of possible selections.
210
