Deck 7: Basic Probability Theory

Question 1

According to set theory, a set is a well-defined collection of things and objects but not events.

Answer 1

False

Question 2

A subset of a larger set is also considered to be the universal set.

Answer 2

False

Question 3

The gambler's fallacy involves treating events that are independent of each other as dependent.

Answer 3

True

Question 4

On tossing a coin, the probability of obtaining an outcome of HHHHHH is smaller than the probability of obtaining an outcome of HTHHHT.

Question 5

The gambler's fallacy usually results in a correct judgement of probability of an outcome, even though the calculation of probability is not exactly correct.

Question 6

The probability of a given event that depends on the occurrence or non-occurrence of another event is known as conditional probability.

Question 7

Consider 3 sets of events. As long as all three sets do not overlap, we can consider them mutually exclusive.

Question 8

True or False: When there are five events in which the occurrence of one (event A) alters the probability of the occurrence of all the rest (events B, C, D, E), then events B, C, D and E are known as dependent on event A.

Question 9

Another term for events that are mutually exclusive is disjoint.

Question 10

When two events are mutually exclusive, it means that when one occurs, the other event cannot occur.

Question 11

The gambler's fallacy is also known as the Monte Carlo fallacy.

Question 12

An empirical set is a set of theoretical predictions.

Question 13

The probability of obtaining two sixes after rolling two dice is the same regardless of whether you roll the dice sequentially or simultaneously.

Question 14

When calculating the probability of obtaining a tail after a toss of a coin, the denominator of the formula is the number of events in a universal set.

Question 15

To calculate the probability of two independent events occurring, we add the probabilities of the occurrence of each event.

Question 16

The law of large numbers is a fallacy that results in an overestimation of the frequency of extreme outcomes.

Question 17

The probability of obtaining a 2, 4, or 5 on a roll of a die is the same as the probability of obtaining an odd number.

Question 18

In the law of large numbers, the "large numbers" refers to anything larger than 100.

Question 19

The probability of obtaining a particular data point is the frequency of it occurring in the population.

Question 20

Inferential statistics allow you to evaluate whether a hypothesis is true or false.

Question 21

How many events are there in a single toss of a coin?

A) 0
B) 0.5
C) 1
D) 2

Question 22

Which of the following options is true?

A) Heads and tails are not considered to be the universal set of outcomes of a toss of a coin because they are only two outcomes.
B) If we toss two dice a single time, the universal set is 6 times 6.
C) A universal set is always made up of interval data.
D) None of the above.

Question 23

Freddie tosses a fair coin 3 times and gets T T T. What is the probability of obtaining tails if he tosses the coin for the fourth time?

A) 100%
B) 50%
C) 25%
D) 10%

Question 24

Lenard studies the relationship between aggressive behavior and finger length. He hypothesizes that the relative length of the index finger to the ring finger predicts aggression. The length of the population of human index finger can be considered the _________________ , while the sample length of the index finger measured from 10 of Lenard's volunteer participants is the _____________.

A) subset; universal set
B) universal subset; semiset
C) semiset; universal subset
D) universal set; subset

Question 25

What is the denominator for calculating the probability of drawing a Queen from a deck of cards after first having drawn a King with no replacement?

A) 52
B) 51
C) 4
D) 48

Question 26

What is the probability that when drawing a card at random from the deck, it will be the queen of hearts?

A) 0.2%
B) 1%
C) 2%
D) 4%

Question 27

Consider a black bag of colored plastic cubes, with 5 red cubes and 6 blue cubes. The probability of randomly drawing a red cube after having drawn a blue cube is:

A) An independent probability
B) A universal probability
C) A normalized probability
D) A conditional probability

Question 28

Which of the following best describes mutual exclusivity?

A) Drawing an ace after having previously drawn an ace from a deck of cards.
B) Obtaining tails on a single toss of a coin.
C) A very small probability that occurs on the tail ends of the normal distribution.
D) Events that are independent from each other.

Question 29

A newly discovered species of rats can have blue eyes, brown eyes or black eyes. Both eyes of a rat have to be the same color. This means that blue, brown and black eye color are:

A) Disjoint
B) Independent
C) Dependent
D) Empirical

Question 30

What is the probability that when drawing a card at random from the deck, it will not be the King of Clubs?

A) 98%
B) 95%
C) 92%
D) 90%

Question 31

What is the universal set of the outcomes of tossing a regular die?

A) The hypothetical outcome that you actually obtain on that single throw.
B) Numbers one to six.
C) Obtaining the number that you guessed, or not obtaining the number that you guess.
D) None of the above.

Question 32

Which of the following is an example of the law of large numbers?

A) The gambler's fallacy
B) Mutual exclusivity of whether heads or tails are obtained on a single toss of a coin
C) In the long run, the chances of obtaining heads from tossing a fair coin is 0.5.
D) The empirical probability of obtaining a 6 after ten tosses of a fair die.

Question 33

When rolling a die, what is the probability of obtaining an odd number on a single throw?

A) 1/3
B) 1/6
C) ½
D) 1/5

Question 34

In a deck of 52 cards, what is the probability of drawing either a two or a three on the first draw?

A) 8%
B) 64%
C) 0.6%
D) 15%

Question 35

In a deck of 52 cards, what is the probability of not drawing a five on the first draw?

A) 8%
B) 25%
C) 92.3%
D) 87%

Question 36

For the empirical probability of roulette outcomes to approach the theoretical probability, the number of trials has to be approaching infinity. This is also known as:

A) The gambler's fallacy
B) The law of large numbers
C) The universal set
D) Inferential statistics

Question 37

In a set of 3 possible events that are mutually exclusive, what is the probability of two different events occurring together?

A) 0
B) 0.33
C) 0.11
D) 0.66

Question 38

The theoretical probability of drawing two black cards simultaneously from a deck of poker cards is:

A) 25%
B) 75%
C) 100%
D) 50%

Question 39

Reba tosses a coin 20 times. She obtains 14 heads and 6 tails. Reba concludes that this coin is not a fair coin. Which of the following is true?

A) Reba is probably right, because if the coin were fair, she would have obtained exactly 10 heads and 10 tails.
B) Reba is probably right if the outcome of heads cluster together instead of being spread out.
C) Reba is probably wrong, because theoretical probability never happens in real life.
D) Reba is probably wrong, because empirical probability approaches theoretical probability only with an infinitely large number of tosses.

Question 40

Elliot draws two cards randomly from a deck of 52 cards. What is the probability that both cards are Kings?

A) 0.8%
B) 0.1%
C) 0.6%
D) 0.5%

Question 41

Consider the 12 face cards from a deck of playing cards (king, queen, and jack). Ben draws three cards from these face cards with replacement. What it the probability that he draws at least one Jack?

A) 1.7%
B) 70.4%
C) 8.3%
D) 15%

Question 42

Penny tosses two dice. What is the probability that both dice are the exact same number?

A) 17%
B) 3%
C) 33%
D) 13%

Question 43

What is the probability of drawing either a black card or a King on the first draw from a deck of 52 cards?

A) 4%
B) 54%
C) 50%
D) 71%

Question 44

Which of the following statements is true?

A) In a sport with wins, losses and draws, a win is considered a mutually exclusive event.
B) In a sport with wins, losses and draws, a win is considered an independent event from a loss.
C) In a casino, roulette allows you to beat the House in the long run as long as you have enough money.
D) In a casino, when the probability of winning favors the House, then the gambler's fallacy is at play.

Question 45

Veronica tosses three dice. What is the probability that none of the dice rolls a 1?

A) 50%
B) 52%
C) 55%
D) 58%

Question 46

Define the gambler's fallacy and give an example of how it can lead to a wrong conclusion.

Question 47

Nadia tosses a fair coin 3 times. She is surprised to find that the outcome is H H H. Nadia claims that this is not a fair coin. Do you agree? Why or why not?

Question 48

Consider the 12 face cards in a deck (king, queen and jack). What is the probability of obtaining a spade on the first draw? Explain, or show, how you got the answer.

Question 49

Explain what is meant when a coin is "fair".

Question 50

Randolph has a box with 12 plastic balls. Six of the balls are red and six are green.
-What is the probability of drawing all red balls if you draw three times with replacement?

Question 51

Randolph has a box with 12 plastic balls. Six of the balls are red and six are green.
-What is the probability of drawing all red balls if you draw three times without replacement? Show all the steps in your calculations.