Deck 8: Random Sampling and Probability

Question 1

A "hungry" undergraduate student was looking for a way of making some extra money. The student turned to a life of vice - gambling. To be a good gambler, he needed to know the probability of certain events. Help him out by answering the following question A royal flush in poker is when you end up with the ace, king, queen, jack, and 10 of the same suit. It's the most rare event in poker. If you are playing with a well- shuffled, legitimate deck of 52 cards, what is the probability that if you are dealt 5 cards, you will have a royal flush? Assume randomness.

A) 0.0000000032
B) 0.000000013
C) 0.0000015
D) 0.0000004

Answer 1

0.000000013

Question 2

Probabilities vary between _________.

A) 0 and 2
B) 0 and 100
C) - 1 and 0
D) 0 and 1

Answer 2

0 and 1

Question 3

If the odds in favor of an event occurring are 9 to 1, the probability of the event occurring is _________.

A) 9
B) 1/9
C) 9/10
D) 8/9

Answer 3

9/10

Question 4

A "hungry" undergraduate student was looking for a way of making some extra money. The student turned to a life of vice - gambling. To be a good gambler, he needed to know the probability of certain events. Help him out by answering the following question. The probability of drawing an ace, a king and a queen of any suit in that order is _________. Sampling is without replacement from a deck of 52 ordinary playing cards.

A) 0.00045
B) 0.00046
C) 0.00048
D) 0.00018

Question 5

Two events are independent if _________.

A) the occurrence of one has no effect on the probability of occurrence of the other
B) the occurrence of one precludes the occurrence of the other
C) the occurrence of one substantially alters the probability of occurrence of the other
D) the sum of their probabilities equals one
E) the occurrence of one has no effect on the probability of occurrence of the other and the sum of their probabilities equals one

Question 6

If A and B are mutually exclusive and exhaustive, then p ( A and B ) = _________.

A) 1
B) 0
C) p ( A ) + p ( B )
D) p ( A ) + p ( B ) - p ( A and B )

Question 7

If events A and B are independent, then p ( A and B ) = _________.

A) p ( A ) + p ( B ) - p ( A and B )
B) p ( A ) p ( B )
C) p ( A or B )
D) 0

Question 8

A "hungry" undergraduate student was looking for a way of making some extra money. The student turned to a life of vice - gambling. To be a good gambler, he needed to know the probability of certain events. Help him out by answering the following question. The probability of drawing 3 aces in a row without replacement from a deck of 52 ordinary playing cards is _________.

A) 0.00018
B) 0.00046
C) 0.00017
D) 0.00045

Question 9

Two events are mutually exclusive if _________.

A) they are independent
B) they both cannot occur together
C) the occurrence of one slightly alters the probability of occurrence of the other
D) the probability of their joint occurrence equals one

Question 10

A sample is random if _________.

A) each possible sample of a given size has an equal chance of being selected
B) all members of the population have an equal chance of being selected into the sample
C) all members of the sample have an equal chance of being selected
D) a, or a and b
E) a and c

Question 11

The Addition Rule states _________.

A) p ( A or B ) = p ( A ) + p ( B ) - p ( A and B )
B) p( A and B ) = p ( A ) p ( B | A )
C) P + Q = 1
D) p ( A ) p ( B | A ) = p ( A ) p (B)

Question 12

A famous hypnotist performs in Meany Hall before a crowd of 350 students and 180 non-students. The hypnotist knows from previous experience that one-half of the students and two-thirds of the non-students are hypnotizable. What is the probability that a randomly chosen person from the audience will be hypnotizable or will be a non-student?

A) 0.330
B) 0.340
C) 0.869
D) 0.670

Question 13

A "hungry" undergraduate student was looking for a way of making some extra money. The student turned to a life of vice - gambling. To be a good gambler, he needed to know the probability of certain events. Help him out by answering the following question. The probability of rolling "boxcars" (two sixes) with one roll of a pair of fair dice is _________.

A) 0.167
B) 0.333
C) 0.033
D) 0.028

Question 14

A "hungry" undergraduate student was looking for a way of making some extra money. The student turned to a life of vice - gambling. To be a good gambler, he needed to know the probability of certain events. Help him out by answering the following question. The probability of drawing a face card (king, queen or jack) of any suit from a deck of 52 ordinary playing cards in one draw is _________.

A) 0.020
B) 0.231
C) 0.077
D) 0.019

Question 15

A set of events is exhaustive if _________.

A) the sum of their probabilities equals one
B) the set includes all of the possible events
C) they are mutually exclusive
D) they are independent

Question 16

Suppose you are going to randomly order individuals A , B , C , D , E and F . The probability the order will begin A B _ _ _ _ is _________.

A) 1.000
B) 0.033
C) 0.027
D) 0.000

Question 17

A posteriori probability refers to _________.

A) a probability value deduced from reason alone
B) low priority probability
C) a probability value determined after collecting data
D) none of these

Question 18

A priori probability refers to _________.

A) a probability value deduced from reason alone
B) the highest priority probability
C) a probability value determined after collecting data
D) none of these

Question 19

Captain Kirk and Mr. Spock are engaged in a 3-D backgammon playoff, a game employing 6 dice. Kirk asks Spock the probability of rolling the dice and observing 6 sixes. Assume the dice are not biased. Spock's correct a priori reply is _________.

A) "Insufficient data, Captain."
B) "One-sixth to the sixth power, Sir." Translation: (1/6) 6
C) "One-thirtysixth, Sir."
D) "One-thirtysix to the sixth power, Sir." (1/36) 6
E) "The probability is equal to (1/6)X(1/5)X(1/4)X(1/3)X (1/2)X(1/1), Sir." (1/720)

Question 20

The Multiplication Rule states _________.

A) p ( A or B ) = p ( A ) + p ( B ) - p ( A and B )
B) p ( A or B ) = p ( A ) + p ( B )
C) p ( A and B ) = p ( A ) p ( B | A )
D) p ( A and B ) = p ( A ) + p ( B )

Question 21

Let's assume you are having a party and have stocked your refrigerator with beverages. You have 12 bottles of Coors beer, 24 bottles of Rainier beer, 24 bottles of Schlitz light beer, 12 bottles of Hamms beer, 2 bottles of Heineken dark beer and 6 bottles of Pepsi soda. You go to the refrigerator to get beverages for your friends. In answering the following question assume you are randomly sampling without replacement. What is the probability the first four bottles you select will be a Coors, a Schlitz, a Rainier, and a Coors in that order?

A) 0.0020
B) 0.0022
C) 0.8875
D) 0.0019

Question 22

A certain university maintains a colony of male mice for research purposes. The ages of the mice are normally distributed with a mean of 60 days and a standard deviation of 5.2. Assume you randomly sample one mouse from the colony. The probability his age will be greater than 68 is _________.

A) 0.4382
B) 0.0618
C) 0.9382
D) 0.0630

Question 23

The probability of randomly selecting a face card (K, Q, or J) or a spade in one draw equals _________.

A) 0.0192
B) 0.0577
C) 0.4808
D) 0.4231

Question 24

If µ = 35.2 and s = 10, then p ( X ) for X ≤ 39 equals _________. Assume random sampling.

A) 0.3520
B) 0.6200
C) 0.1480
D) 0.6480

Question 25

If p ( A or B ) = p ( A ) + p ( B ) then A and B must be _________.

A) dependent
B) mutually exclusive
C) overlapping
D) continuous

Question 26

A certain university maintains a colony of male mice for research purposes. The ages of the mice are normally distributed with a mean of 60 days and a standard deviation of 5.2. Assume you randomly sample one mouse from the colony. The probability his age will be between 55 and 70 days is _________.

A) 0.8041
B) 0.4980
C) 0.8066
D) 0.1959

Question 27

If P + Q = 1.00 then P and Q must be _________.

A) mutually exclusive
B) exhaustive
C) random
D) both mutually exclusive and exhaustive

Question 28

Let's assume you are having a party and have stocked your refrigerator with beverages. You have 12 bottles of Coors beer, 24 bottles of Rainier beer, 24 bottles of Schlitz light beer, 12 bottles of Hamms beer, 2 bottles of Heineken dark beer and 6 bottles of Pepsi soda. You go to the refrigerator to get beverages for your friends. In answering the following question assume you are randomly sampling without replacement. What is the probability the first bottle selected is a Coors beer?

A) 0.0750
B) 0.1500
C) 0.3000
D) 0.1622

Question 29

Let's assume you are having a party and have stocked your refrigerator with beverages. You have 12 bottles of Coors beer, 24 bottles of Rainier beer, 24 bottles of Schlitz light beer, 12 bottles of Hamms beer, 2 bottles of Heineken dark beer and 6 bottles of Pepsi soda. You go to the refrigerator to get beverages for your friends. In answering the following question assume you are randomly sampling without replacement. What is the probability your first three bottles selected are Pepsi's?

A) 0.00044
B) 0.00024
C) 0.1875
D) 0.2250

Question 30

If a town of 7000 people has 4000 females in it, then the probability of randomly selecting 6 females in six draws (with replacement) equals _________.

A) 0.0348
B) 0.0571
C) 0.5714
D) 0.3429

Question 31

If a stranger gives you a coin and you toss it 1,000,000 times and it lands on heads 600,000 times, what is p (Heads) for that coin?

A) 0.5000
B) 0.6000
C) 0.4000
D) 0.0000

Question 32

The probability of throwing two ones with a pair of dice equals _________.

A) 0.3600
B) 0.1667
C) 0.0278
D) 0.3333

Question 33

The probability of drawing an ace followed by a king (without replacement) equals _________.

A) 0.0044
B) 0.0060
C) 0.0045
D) 0.0965

Question 34

A certain university maintains a colony of male mice for research purposes. The ages of the mice are normally distributed with a mean of 60 days and a standard deviation of 5.2. Assume you randomly sample one mouse from the colony. The probability his age will be less than 45 days is _________.

A) 0.9980
B) 0.4980
C) 0.0020
D) 0.0019

Question 35

Assume you are rolling two fair dice once . The probability of obtaining a sum of 2 or 12 equals _________.

A) 0.0228
B) 0.3333
C) 0.0833
D) 0.0556

Question 36

Which of the following are examples of mutually exclusive events?

A) rain and a cloudless sky
B) snow and a temperature of 10 ° Celsius
C) walking and running at the same time
D) all of these

Question 37

Let's assume you are having a party and have stocked your refrigerator with beverages. You have 12 bottles of Coors beer, 24 bottles of Rainier beer, 24 bottles of Schlitz light beer, 12 bottles of Hamms beer, 2 bottles of Heineken dark beer and 6 bottles of Pepsi soda. You go to the refrigerator to get beverages for your friends. In answering the following question assume you are randomly sampling without replacement. What is the probability the first beverage you get is a beer?

A) 0.9250
B) 0.9000
C) 0.9487
D) 0.7750

Question 38

If p ( A and B ) = 0, then A and B must be _________.

A) independent
B) mutually exclusive
C) exhaustive
D) unbiased

Question 39

Assume you are rolling two fair dice once . The probability of obtaining at least one 3 or one 4 equals _________.

A) 0.3333
B) 0.5556
C) 0.1111
D) 0.0833

Question 40

Assume you are rolling two fair dice once . The probability of obtaining a sum of 5 equals _________.

A) 0.3333
B) 0.0228
C) 0.1111
D) 0.0556

Question 41

A random sample results when each possible sample of a given size has an equal chance of being selected.

Question 42

When events A and B are mutually exclusive but not exhaustive, p ( A or B ) equals _________.

A) 0.50
B) 0.00
C) 1.00
D) cannot be determined from the information given

Question 43

The Multiplication Rule concerns the joint or successive occurrence of several events.

Question 44

If events are mutually exclusive they cannot be _________.

A) independent
B) exhaustive
C) related
D) all the above

Question 45

The Addition Rule concerns one of several possible events.

Question 46

If p ( A ) p ( B | A ) = p ( A ) p ( B ), then A and B must be _________.

A) independent
B) mutually exclusive
C) random
D) exhaustive

Question 47

If a set of events is exhaustive, they only constitute a part of the possible events.

Question 48

The probability of rolling an even number or a one on a throw of a single die equals _________.

A) 0.6667
B) 0.5000
C) 0.0834
D) 0.3333

Question 49

If p ( A and B ) = p ( A ) p ( B | A ) ≠ p ( A ) p ( B ), then A and B are _________.

A) mutually exclusive
B) random
C) independent
D) dependent

Question 50

If µ = 400 and s = 100 the probability of selecting at random a score less than or equal to 370 equals _________.

A) 0.1179
B) 0.6179
C) 0.3821
D) 0.8821

Question 51

For all problems, we must use either the Addition Rule or the Multiplication Rule, but not both.

Question 52

The probability of correctly calling 4 tosses of an unbiased coin in a row equals _________.

A) 0.0625
B) 0.5000
C) 0.1250
D) 0.2658

Question 53

Probability values range from 0 to 1.

Question 54

A priori and a posteriori probability have the same meaning.

Question 55

If two events are mutually exclusive, they must be dependent.

Question 56

If the probability of drawing a member of a population is not equal for all members, then the sample is said to be _________.

A) random
B) independent
C) exhaustive
D) biased

Question 57

When a sampled score is put back in the population before selecting the next score, this process is called sampling without replacement.

Question 58

If you have 15 red socks (individual, not pairs), 24 green socks, 17 blue socks, and 100 black socks, what is the probability you will reach in the drawer and randomly select a pair of green socks? (Assume sampling without replacement.)

A) 0.3022
B) 0.3077
C) 0.0228
D) 0.0227

Question 59

The probability of correctly guessing a two digit number is _________.

A) 0.1000
B) 0.0100
C) 0.2000
D) 0.5000

Question 60

If p ( A ) = 0.6 and p ( B ) = 0.5, then p ( B | A ) equals _________.

A) 0.8333
B) 0.3000
C) 0.5000
D) cannot be determined from the information given

Question 61

Two events are considered mutually exclusive if the probability of one event does not influence the probability of a second event.

Question 62

If an event is certain to occur, its probability of occurrence equals 1.00.

Question 63

Sampling without replacement is usually used in choosing subjects for an independent groups design experiment.

Question 64

Events that occur only rarely have a probability equal to 0.00.

Question 65

When events are mutually exclusive and exhaustive then the sum of the individual probabilities of each event in the set must equal 1.00.

Question 66

If an event is certain not to occur, its probability of occurrence equals 0.00.

Question 67

In order to generalize to the population a sample must be randomly selected.

Question 68

An a posteriori approach to probability is never used because it is only an approximation of the true probability.

Question 69

When two events are dependent, then p ( A and B ) = p ( A ) + p ( B ).

Question 70

For a sample to be random, all the members must have an equal chance of being selected into the sample.

Question 71

Hypothesis testing is part of inferential statistics while parameter estimation is used in descriptive statistics.

Question 72

Probability values range from - 1.00 to +1.00.

Question 73

The addition rule is concerned with determining the probability of A or B , while the multiplication rule is concerned with determining the probability A and B .

Question 74

When a variable is continuous, p ( A ) equals the area under the curve corresponding to A divided by the total area under the curve.

Question 75

To use a random number table properly one must begin on the top left hand column and read across.

Question 76

p ( B | A ) is read probability of B divided by A .

Question 77

When two events are mutually exclusive then p ( A and B ) must equal 1.00.

Question 78

If two events are mutually exclusive and exhaustive, P + Q = 1.

Question 79

If sampling is without replacement, the events are independent.

Question 80

Two events are independent if the occurrence of one has no effect on the probability of occurrence of the other.