If A and B are independent events with P(A) = .38 and P(B) = .55, then P(A | B) =
| a. .550 |
| b. .38 |
| c. 0 |
| d. .209 |
The symbol ∩ shows the _____.
| a. union of events |
| b. intersection of events |
| c. sum of the probabilities of events |
| d. sample space of events |
Any process that generates well-defined outcomes is _____.
| a. an event |
| b. a sample point |
| c. a probability |
| d. an experiment |
In an experiment, events A and B are mutually exclusive. If P(A) = 0.35, then the probability of B _____.
| a. can be any value greater than 0.35 |
| b. must also be 0.35 |
| c. can be any value between 0 and 1 |
| d. cannot be larger than 0.65 |
If A and B are independent events with P(A) = 0.4 and P(B) = 0.5, then _____.
| a. P(A ∩ B) = 0.20 |
| b. P(A ∩ B) = 0 |
| c. P(A ∩ B) = 0.45 |
| d. P(A ∩ B) = 0.90 |
If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) =
| a. .30 |
| b. .15 |
| c. 0 |
| d. .20 |
If P(A) = 0.68, P(B) = 0.49, and P(A ∪ B) = 0.82; then P(A ∩ B) = _____.
| a. 0.333 |
| b. 0.35 |
| c. 0.47 |
| d. 1.99 |
If A and B are mutually exclusive events with P(A) = 0.10 and P(B) = 0.85, then P(A ∪ B) = _____.
| a. 0.05 |
| b. 0 |
| c. 0.75 |
| d. 0.95 |
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 _____.
| a. 14 |
| b. 9 |
| c. 36 |
| d. 24 |
An experiment consists of tossing four coins successively. The number of sample points in this experiment is _____.
| a. 4 |
| b. 8 |
| c. 16 |
| d. 2 |
If A and B are independent events with P(A) = .38 and P(B) = .55, then P(A | B) =
| a. .550 |
| b. .209 |
| c. 0 |
| d. .38 |
If A and B are mutually exclusive events with P(A) = .5 and P(B) = .5, then P(A ∩ B) is _____.
| a. .25 |
| b. .5 |
| c. 0 |
| d. 1 |
Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following three customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is _____.
| a. 2 |
| b. 8 |
| c. 4 |
| d. 6 |
A(n) __________ is a collection of sample points.
| a. permutation |
| b. experiment |
| c. event |
| d. probability |
If P(A) = .85, P(B) = .76, and P(A ∩ B) = .72, then P(A | B) = _____.
| a. .95 |
| b. .25 |
| c. .15 |
| d. .53 |
An experiment consists of four outcomes with P(E 1) = 0.4, P(E 2) = 0.2, and P(E 3) = 0.1. The probability of outcome E 4 is _____.
| a. 0.600 |
| b. 0.300 |
| c. 0.008 |
| d. 0.700 |
You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.
| a. mutually exclusive events |
| b. independent events |
| c. complements |
| d. posterior events |
An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____.
| a. .500 |
| b. .900 |
| c. .024 |
| d. .100 |
A sample point refers to a(n) _____.
| a. individual outcome of an experiment |
| b. initial estimate of the probabilities of an event |
| c. numerical measure of the likelihood of the occurrence of an event |
| d. set of all possible experimental outcomes |
Suppose we flip a fair coin five times and each time it lands heads up. The probability of landing heads up on the next flip is _____.
| a. .5 |
| b. .75 |
| c. 1 |
| d. 0 |
The symbol ∪ indicates the _____.
| a. intersection of events |
| b. union of events |
| c. sample space |
| d. sum of the probabilities of events |
A graphical method of representing the sample points of a multiple-step experiment is a(n) _____.
| a. tree diagram |
| b. frequency polygon |
| c. histogram |
| d. ogive |
You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.
| a. posterior events |
| b. independent events |
| c. mutually exclusive events |
| d. complements |
One of the basic requirements of probability is _____.
| a. P(A) = P(Ac) |
| b. if there are k experimental outcomes, then P(E1) + P(E2) + … + P(Ek) = 1 |
| c. for each experimental outcome Ei, we must have P(Ei) ≥ 1 |
| d. P(A) = P(Ac) – 1 |
Revised probabilities of events based on additional information are _____.
| a. marginal probabilities |
| b. complementary probabilities |
| c. posterior probabilities |
| d. joint probabilities |
The collection of all possible sample points in an experiment is _____.
| a. the sample space |
| b. a sample point |
| c. the population |
| d. an experiment |
The symbol ∩ shows the _____.
| a. sample space of events |
| b. intersection of events |
| c. sum of the probabilities of events |
| d. union of events |
If A and B are mutually exclusive, then _____.
| a. P(A ∩ B) = 1 |
| b. P(A) + P(B) = 0 |
| c. P(A ∩ B) = 0 |
| d. P(A) + P(B) = 1 |
In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____.
| a. can be any value greater than .6 |
| b. can be any value between 0 and 1 |
| c. cannot be larger than .4 |
| d. must also be .6 |
If A and B are independent events with P(A) = .05 and P(B) = .65, then P(A | B) = _____.
| a. .8 |
| b. .65 |
| c. .0325 |
| d. .05 |
Two events are mutually exclusive if _____.
| a. the probability of their intersection is 1 |
| b. they have no sample points in common |
| c. the probability of their intersection is .5 |
| d. the probability of their intersection is 1 and they have no sample points in common |
If A and B are independent events with P(A) = 0.2 and P(B) = 0.45, then P(A ∪ B) = _____.
| a. 0.89 |
| b. 0.09 |
| c. 0.65 |
| d. 0.56 |
A method of assigning probabilities based upon judgment is referred to as the _____.
| a. probability method |
| b. relative frequency method |
| c. classical method |
| d. subjective method |
Two events with nonzero probabilities _____.
| a. cannot be both mutually exclusive and independent |
| b. are always mutually exclusive |
| c. can be both mutually exclusive and independent |
| d. are always independent |
Of the last 100 customers entering a computer shop, 72 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is _____.
| a. 0.50 |
| b. 1 |
| c. 0.28 |
| d. 0.72 |
Bayes’ theorem is used to compute _____.
| a. the posterior probabilities |
| b. the union of events |
| c. the intersection of events |
| d. the prior probabilities |
The range of probability is _____,
| a. any value between –1 to 1 |
| b. any value larger than 0 |
| c. 0 to 1, inclusive |
| d. any value between minus infinity to plus infinity |
Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is _____.
| a. .25 |
| b. .50 |
| c. 1 |
| d. .75 |
The probability of at least one head in two flips of a coin is _____.
| a. .33 |
| b. 1 |
| c. .75 |
| d. .50 |
A(n) __________ is a collection of sample points.
| a. event |
| b. experiment |
| c. probability |
| d. permutation |
Given that event E has a probability of .25, the probability of the complement of event E _____.
| a. cannot be determined with the above information. |
| b. can have any value between 0 and 1 |
| c. must be .75 |
| d. is .25 |
There is a 60% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?
| a. .60 |
| b. 1.20 |
| c. .30 |
| d. .36 |
If P(A) = .85, P(B) = .76, and P(A ∩ B) = .72, then P(A | B) = _____.
| a. .95 |
| b. .15 |
| c. .53 |
| d. .25 |
If P(A | B) = 0.5 and P(B) = 0.7, then _____.
| a. P(A ∩ B) = 0.35 |
| b. P(A ∩ B) = 0.20 |
| c. P(B | A) = 0.85 |
| d. P(A) = 0.35 |
If X and Y are mutually exclusive events with P(X) = .295, P(Y) = .32, then P(X ∩ Y) = _____.
| a. .615 |
| b. .094 |
| c. 0 |
| d. 1 |
A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least five spots will be showing up on the die?
| a. 0.5 |
| b. 0.667 |
| c. 0.333 |
| d. 0.167 |
In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____.
| a. can be any value greater than .6 |
| b. can be any value between 0 and 1 |
| c. cannot be larger than .4 |
| d. must also be .6 |
Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____.
| a. .06 |
| b. .80 |
| c. 0 |
| d. .70 |
If A and B are independent events with P(A) = 0.3 and P(B) = 0.9, then P(A ∪ B) = _____.
| a. 0.87 |
| b. 0.93 |
| c. 0.27 |
| d. 0.90 |
Events A and B are mutually exclusive with P(A) = 0.50 and P(B) = 0.40. The probability of the complement of event B equals _____.
| a. 0 |
| b. 0.60 |
| c. 0.50 |
| d. 0.20 |
Twenty percent of people at a company picnic got food poisoning. What percent of the people at the picnic did NOT get food poisoning?
| a. 20% |
| b. 60% |
| c. 80% |
| d. 40% |
If A and B are mutually exclusive events with P(A) = 0.10 and P(B) = 0.75, then P(A ∩ B) = _____.
| a. 0.05 |
| b. 0.65 |
| c. 0 |
| d. 0.10 |
Events A and B are mutually exclusive with P(A) = 0.20 and P(B) = 0.10. The probability of the complement of event B equals _____.
| a. 0 |
| b. 0.90 |
| c. 0.80 |
| d. 0.02 |
If A and B are independent events with P(A) = .38 and P(B) = .55, then P(A | B) =
| a. .550 |
| b. .209 |
| c. .38 |
| d. 0 |
If a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is _____.
| a. .20 |
| b. .50 |
| c. .03125 |
| d. 0 |
The union of events A and B is the event containing _____.
| a. all the sample points belonging to A or B |
| b. all the sample points belonging to A or B or both |
| c. all the sample points belonging to A or B, but not both |
| d. all the sample points common to both A and B |
If A and B are mutually exclusive events with P(A) = .3 and P(B) = .5, then P(A ∪ B) =
| a. 0 |
| b. .2 |
| c. .8 |
| d. .15 |
If P(A) = .75, P(A ∪ B) = .86, and P(A ∩ B) = .56, then P(B) =
| a. .11 |
| b. .67 |
| c. .56 |
| d. .25 |
Posterior probabilities are computed using _____.
| a. Chebyshev’s theorem |
| b. the classical method |
| c. the empirical rule |
| d. Bayes’ theorem |
There is a 70% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?
| a. 0.49 |
| b. 0.70 |
| c. 1.40 |
| d. 0.35 |
An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____.
| a. .024 |
| b. .100 |
| c. .900 |
There is a 60% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?
| a. .36 |
| b. .60 |
| c. 1.20 |
| d. .30 |
If a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is _____.
| a. .03125 | |||||||
| b. .20 | |||||||
| c. 0 | |||||||
| d. .50 | |||||||
| A | B | C | D | E | |||
| 1 | Prior | Conditional | Joint | ||||
| 2 | Event | Probability | Probability | Probability | |||
| 3 | A1 | 0.25 | 0.31 | ||||
For the Excel worksheet above, which of the following formulas would correctly calculate the joint probability for cell D3?
| a. =B3*C3 |
| b. =B3+C3 |
| c. =B3/C3 |
| d. =SUM(B3:C3) |
A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least three spots will be showing up on the die?
| a. .67 |
| b. .5 |
| c. .3 |
| d. .167 |
The probability of the union of two events with nonzero probabilities cannot be _____.
| a. less than 1 |
| b. less than one and cannot be 1 |
| c. 1 |
| d. more than 1 |
If P(A | B) = 0.4, _____.
| a. P(A c | B) = 0.6 |
| b. P(A c | B c) = 0.6 |
| c. P(B | A) = 0.6 |
| d. P(A | B c) = 0.6 |
Two events are mutually exclusive if _____.
| a. the probability of their intersection is .5 |
| b. the probability of their intersection is 1 |
| c. they have no sample points in common |
| d. the probability of their intersection is 1 and they have no sample points in common |
If A and B are independent events with P(A) = 0.1 and P(B) = .4, then _____.
| a. P(A ∩ B) = .04 |
| b. P(A ∩ B) = .5 |
| c. P(A ∩ B) = 0 |
| d. P(A ∩ B) = .25 |
The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many “Top Three” outcomes are there?
| a. 1,814,400 |
| b. 302,400 |
| c. 10 |
| d. 720 |
The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed two times and event A did not occur, then on the third trial event A _____.
| a. has a 2/3 probability of occurring |
| b. may occur |
| c. must occur |
| d. could not occur |
The multiplication law is potentially helpful when we are interested in computing the probability of _____.
| a. the intersection of two events |
| b. mutually exclusive events |
| c. the complement of an event |
| d. the union of two events |
If A and B are independent events with P(A) = 0.1 and P(B) = .4, then _____.
| a. P(A ∩ B) = .04 |
| b. P(A ∩ B) = .25 |
| c. P(A ∩ B) = 0 |
| d. P(A ∩ B) = .5 |
The range of probability is _____,
| a. any value larger than 0 |
| b. any value between –1 to 1 |
| c. 0 to 1, inclusive |
| d. any value between minus infinity to plus infinity |
The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many “Top Three” outcomes are there?
| a. 302,400 |
| b. 1,814,400 |
| c. 720 |
| d. 10 |
There is a 40% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?
| a. 0.80 |
| b. 0.40 |
| c. 0.20 |
d. 0.16 |
If P(A) = 0.50, P(B) = 0.46, and P(A ∩ B) = 0.35, then P(B | A) = _____.
| a. 0.7000 |
| b. 0.7609 |
| c. 0.6100 |
| d. 0.9200 |
If A and B are mutually exclusive, then _____.
| a. P(A) + P(B) = 1 |
| b. P(A ∩ B) = 1 |
| c. P(A ∩ B) = 0 |
d. P(A) + P(B) = 0 |
If P(A ∩ B) = 0, _____.
| a. A and B are mutually exclusive events |
| b. A and B are independent events |
| c. P(A) + P(B) = 1 |
| d. either P(A) = 0 or P(B) = 0 |
A six-sided die is rolled three times. The probability of observing a 1 three times in a row is _____.
| a. .16 |
| b. .3 |
| c. .004629 |
| d. .037 |
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
| Number of Goals | Probability |
| 0 | 0.10 |
| 1 | 0.15 |
| 2 | 0.10 |
| 3 | 0.30 |
| 4 | 0.35 |
What is the probability that in a given game the Lions will score less than 2 goals?
| a. 0.25 |
| b. 0.75 |
| c. 0.35 |
| d. 0.10 |
The standard deviation of a binomial distribution is _____.
| a. E(x) = np |
| b. E(x) = np(1 − p) |
| c. E(x) = pn(1 − n) |
d. the positive square root of the variance |
A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
| a. .0004 |
| b. .0038 |
| c. .10 |
| d. .02 |
The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages ( x ) in the city has the following probability distribution.
| x | f (x) |
| 0 | 0.80 |
| 1 | 0.15 |
| 2 | 0.04 |
| 3 | 0.01 |
The mean and the standard deviation for the number of electrical outages (respectively) are _____.
| a. 2.6 and 5.77 |
| b. 3 and .01 |
| c. 0 and .8 |
| d. 0.26 and .577 |
Variance is _____.
| a. the sum of the deviation of data elements from the mean |
| b. the square root of the standard deviation |
| c. a measure of the dispersion of a random variable |
d. a measure of the average, or central value of a random variable |
The key difference between binomial and hypergeometric distributions is that with the hypergeometric distribution the _____.
| a. trials are independent of each other |
| b. probability of success must be less than .5 |
| c. probability of success changes from trial to trial |
| d. random variable is continuous |
Assume that you have a binomial experiment with p = 0.2 and a sample size of 50. The variance of this distribution is _____.
| a. 8 |
| b. 2 |
| c. 10 |
d. 2.83 |
Exhibit 5-10
The probability Pete will catch fish when he goes fishing is .8. Pete is going fishing 3 days next week.
What is the random variable in this experiment?
| a. the number of days out of 3 that Pete catches fish |
| b. the .8 probability of catching fish |
| c. the 3 days |
| d. the number of fish in the body of water |
Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is _____.
| a. 16 |
| b. 4 |
| c. 2 |
| d. 20 |
When using Excel’s HYPGEOM.DIST function, one should choose TRUE for the fifth input if _____.
| a. a cumulative probability is desired |
| b. the expected value is desired |
| c. a probability is desired |
| d. the correct answer is desired |
The binomial probability distribution is used with _____.
| a. any random variable |
| b. any distribution, as long as it is not bell shaped |
| c. a continuous random variable |
| d. a discrete random variable |
Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
What is the probability that among the students in the sample at least 7 are female?
| a. .1064 |
| b. .0896 |
| c. .0168 |
| d. .893 |
Which of the following is NOT a property of a binomial experiment?
| a. The probabilities of the two outcomes can change from one trial to the next. |
| b. The trials are independent. |
| c. The experiment consists of a sequence of n identical trials. |
| d. Each outcome can be referred to as a success or a failure. |
Exhibit 5-4
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below.
| Number of | |
| Breakdowns | Probability |
| 0 | .12 |
| 1 | .38 |
| 2 | .25 |
| 3 | .18 |
| 4 | .07 |
The expected number of machine breakdowns per month is _____.
| a. 1.70 |
| b. 1 |
| c. 2.50 |
d. 2 |
Exhibit 5-2
The probability distribution for the daily sales at Michael’s Co. is given below.
| Daily Sales ($1000s) | Probability |
| 40 | .1 |
| 50 | .4 |
| 60 | .3 |
| 70 | .2 |
The expected daily sales are _____.
| a. $56,000 |
| b. $55,000 |
| c. $70,000 |
| d. $50,000 |
Exhibit 5-5
AMR is a computer-consulting firm. The number of new clients that it has obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
| Number of | |
| New Clients | Probability |
| 0 | .05 |
| 1 | .10 |
| 2 | .15 |
| 3 | .35 |
| 4 | .20 |
| 5 | .10 |
| 6 | .05 |
The standard deviation is _____.
| a. 2.047 |
| b. 1.431 |
| c. 21 |
| d. 3.05 |
For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is _____.
| a. .9452 |
| b. .0160 |
| c. .0016 |
d. .1600 |
Exponential distributions _____.
| a. can be skewed to the left or right |
| b. are skewed to the right |
| c. are not skewed |
d. are skewed to the left |
For the standard normal probability distribution, the area to the left of the mean is _____.
| a. 1 |
| b. –0.5 |
| c. 0.5 |
| d. any value between 0 and 1 |
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1112?
| a. 3.22 |
| b. 1.22 |
| c. 2.22 |
| d. .3888 |
A property of the exponential distribution is that the mean equals the _____.
| a. variance |
| b. median |
| c. mode |
| d. standard deviation |
About 95.4% of the values of a normal random variable are within approximately how many standard deviations of its mean?
| a. ±1.7 |
| b. ±3 |
| c. ±2.5 |
| d. ±2 |
A standard normal distribution is a normal distribution with _____.
| a. a mean of 1 and a standard deviation of 0 |
| b. any mean and a standard deviation of 1 |
| c. a mean of 0 and a standard deviation of 1 |
d. any mean and any standard deviation |
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