Timedora
Free Practice Quiz Question List

1 Probability Foundations and Sample Spaces Online Quiz Questions

Use this free practice quiz with 20 questions to review 1 Probability Foundations and Sample Spaces, test your knowledge, and prepare for your next test or exam.

20 questions
01
True or false
1 point

True or false: A valid sample space must be complete, mutually exclusive, and detailed enough to answer the question being asked.

  1. A

    True

  2. B

    False

02
Choose one
1 point

Which statement correctly describes an event in probability?

  1. A

    An event must contain exactly one outcome.

  2. B

    An event is a subset of the sample space.

  3. C

    An event must contain every outcome in the sample space.

  4. D

    An event cannot be empty.

03
Written response
1 point

A package arrives on time with probability 0.920.92. What is the probability that it is late?

04
Fill in the blank
1 point

Complete the statements about probability axioms: P(S)=1P(S)=1 is the axiom of , and probabilities of mutually exclusive events obey .

05
Choose one
1 point

A fair six-sided die is rolled once. Let AA be the event of rolling an even number and let BB be the event of rolling a number greater than 3. What is P(A∪B)P(A\cup B)?

  1. A

    13\frac{1}{3}

  2. B

    12\frac{1}{2}

  3. C

    23\frac{2}{3}

  4. D

    56\frac{5}{6}

06
True or false
1 point

True or false: Two events that are mutually exclusive and both have positive probability can also be independent.

  1. A

    True

  2. B

    False

07
Written response
1 point

A card is known to be a heart and is selected from a standard 52-card deck. What is the conditional probability that it is an ace?

08
Fill in the blank
1 point

A meal consists of one of 4 entrees and one of 3 drinks. The number of possible meals is .

09
Choose one
1 point

Which selection problem is an ordered outcome because the roles assigned to the selected people matter?

  1. A

    Selecting a two-person committee from a group

  2. B

    Choosing a president and a vice president from a group

  3. C

    Recording the total number of books borrowed

  4. D

    Selecting one flavor of ice cream

10
Open ended
1 point

Two fair coins are tossed. Determine the probability of getting at least one head. Explain your reasoning using either direct counting or the complement rule.

11
Choose one
1 point

What is the main purpose of a tree diagram in a multistage probability experiment?

  1. A

    It guarantees that all outcomes are equally likely.

  2. B

    It represents stages with branches, with each complete path forming an outcome.

  3. C

    It can be used only for one-stage experiments.

  4. D

    It replaces the need to define what an outcome means.

12
Choose one
1 point

A die is rolled twice, and the first and second rolls are recorded separately. Which description correctly represents the sample space?

  1. A

    S={(1,1),(1,2),…,(6,6)}S=\{(1,1),(1,2),\ldots,(6,6)\}

  2. B

    S={1,2,3,4,5,6}S=\{1,2,3,4,5,6\}

  3. C

    S={2,4,6}S=\{2,4,6\}

  4. D

    S={(1,2),(2,1)}S=\{(1,2),(2,1)\}

13
Choose one
1 point

A fair die is rolled once. Let A={2,4,6}A=\{2,4,6\} and B={4,5,6}B=\{4,5,6\}. What is P(A∪B)P(A\cup B)?

  1. A

    13\frac{1}{3}

  2. B

    12\frac{1}{2}

  3. C

    23\frac{2}{3}

  4. D

    56\frac{5}{6}

14
Choose one
1 point

A card is selected from a standard 52-card deck and is known to be a heart. What is the conditional probability that it is an ace?

  1. A

    152\frac{1}{52}

  2. B

    113\frac{1}{13}

  3. C

    452\frac{4}{52}

  4. D

    14\frac{1}{4}

15
Choose one
1 point

Two cards are drawn from a standard deck without replacement. Which statement best describes the relationship between the two draws?

  1. A

    The draws are independent because every card was initially equally likely.

  2. B

    The draws are independent because the deck has 52 cards.

  3. C

    The draws are mutually exclusive because only one card can be drawn at a time.

  4. D

    The draws are generally dependent because the first draw changes the deck.

16
True or false
1 point

True or false: If two events overlap, their union probability is always P(A)+P(B)P(A)+P(B) without subtracting P(A∩B)P(A\cap B).

  1. A

    True

  2. B

    False

17
Written response
1 point

What is the probability term for a subset of the sample space that describes outcomes of interest?

18
Written response
1 point

Two fair coins are tossed. What is the probability of getting at least one head? Enter your answer as a decimal.

19
Choose all
1 point

Select all situations in which the probability of the stated event can be calculated as the number of favorable outcomes divided by the total number of outcomes.

  1. A

    A fair six-sided die is rolled once, and the event is rolling a number greater than 4.

  2. B

    A biased six-sided die is rolled once, and the event is rolling an even number.

  3. C

    Two fair coins are tossed, with ordered outcomes recorded, and the event is getting at least one head.

  4. D

    A spinner has sectors of unequal sizes, and the event is landing on a red sector.

20
Choose all
1 point

A coin modeled as fair is tossed 100 times, and it lands heads 47 times. Select all conclusions justified by the distinction between empirical and theoretical probability.

  1. A

    The empirical probability of heads in these 100 tosses is 0.47.

  2. B

    The theoretical probability of heads under the fair-coin model is 0.5.

  3. C

    The result proves that the coin is biased.

  4. D

    A fair coin must produce exactly 50 heads in every 100 tosses.

  5. E

    The next 100 tosses are guaranteed to contain exactly 47 heads.