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Free Practice Quiz Question List

6. Probability and Randomness Online Quiz Questions

Use this free practice quiz with 20 questions to review 6. Probability and Randomness, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose one
1 point

A package has probability 0.08 of arriving late. What is the probability that it does not arrive late?

  1. A

    0.08

  2. B

    0.92

  3. C

    1.08

  4. D

    8.00

02
Choose one
1 point

What does the sample space of a random experiment represent?

  1. A

    The set of all possible outcomes

  2. B

    A collection containing only favorable outcomes

  3. C

    The probability assigned to one event

  4. D

    A sequence of conditional probabilities

03
True or false
1 point

True or false: For any two events, P(A∪B)=P(A)+P(B)P(A\cup B)=P(A)+P(B) without any correction for overlap.

  1. A

    True

  2. B

    False

04
True or false
1 point

True or false: If two events are mutually exclusive, their intersection has probability 0.

  1. A

    True

  2. B

    False

05
Written response
1 point

A survey finds that 40% of households subscribe to Service A, 30% subscribe to Service B, and 10% subscribe to both. What is the probability that a randomly selected household subscribes to at least one service? Enter the probability as a decimal.

06
Written response
1 point

In a group of 200 people, 96 use a fitness app and 72 of those 96 exercise regularly. What is the probability that a person exercises regularly given that the person uses the app? Enter the probability as a decimal.

07
Fill in the blank
1 point

The event that both A and B occur is called the , written A∩BA\cap B. The event that A or B or both occur is called the , written A∪BA\cup B.

08
Fill in the blank
1 point

Complete the complement rule: P(Ac)=P(A^c)=.

09
Choose one
1 point

One card is selected from a standard 52-card deck. What is the probability that it is an ace given that it is a heart?

  1. A

    1/52

  2. B

    4/52

  3. C

    1/13

  4. D

    4/13

10
Choose all
1 point

Select all conditions that can be used to establish that events A and B are independent.

  1. A

    P(A∣B)=P(A)P(A\mid B)=P(A), when defined

  2. B

    P(A∩B)=P(A)+P(B)P(A\cap B)=P(A)+P(B)

  3. C

    P(A∩B)=P(A)P(B)P(A\cap B)=P(A)P(B)

  4. D

    P(A∪B)=P(A)P(B)P(A\cup B)=P(A)P(B)

11
Choose all
1 point

Select all situations in which the relevant events may be dependent.

  1. A

    Two fair coin tosses

  2. B

    Two cards drawn without replacement

  3. C

    Two items selected independently from a process with stable probabilities

  4. D

    Two observations affected by the same weather conditions

12
Written response
1 point

A box contains 5 red and 3 blue markers. Two markers are selected without replacement. What is the probability that both are red? Enter the probability as 5/145/14 or as the decimal 0.3571428571428571.

13
Choose one
1 point

In the fitness-app table, why is the denominator 96 when calculating the probability of regular exercise given app use?

  1. A

    200, because that is the total sample size

  2. B

    96, because these are the people who use the app

  3. C

    120, because these are the people who exercise regularly

  4. D

    72, because these are the people satisfying both conditions

14
Open ended
1 point

Explain how to build a probability model for a real-world process and why checking its assumptions is essential. Include a concrete example of how a violated assumption or changed condition could affect the model’s usefulness.

15
Choose one
1 point

A die may land on the table showing 1 through 6, or it may land off the table. Which statement best describes an appropriate sample space for this random process?

  1. A

    The sample space can contain only the most common outcomes.

  2. B

    The sample space should include an off-table result if that result is possible and relevant.

  3. C

    The sample space must assign equal probabilities to all outcomes.

  4. D

    The sample space is the same as the event of rolling an even number.

16
True or false
1 point

True or false: If an event has probability 0.90, it is guaranteed to occur in every individual trial.

  1. A

    True

  2. B

    False

17
Choose one
1 point

A survey finds that 40% of households subscribe to Service A, 30% subscribe to Service B, and 10% subscribe to both. What is the probability that a randomly selected household subscribes to at least one of the two services?

  1. A

    0.30

  2. B

    0.50

  3. C

    0.60

  4. D

    0.70

18
Choose one
1 point

In a group of 200 people, 72 exercise regularly and use a fitness app, while 96 people use a fitness app in total. What is the probability that a person exercises regularly given that the person uses a fitness app?

  1. A

    72/200 = 0.36

  2. B

    72/96 = 0.75

  3. C

    120/200 = 0.60

  4. D

    96/200 = 0.48

19
Choose one
1 point

A box contains 5 red and 3 blue markers. Two markers are selected without replacement. What is the probability that both selected markers are red?

  1. A

    5/8

  2. B

    4/7

  3. C

    5/14

  4. D

    1/2

20
Written response
1 point

One card is selected from a standard 52-card deck. What is the probability that it is an ace given that it is a heart? Enter the probability as a simplified fraction.