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Probability Distributions Practice Tests

These Grade 12 Math practice tests cover discrete and continuous random variables, probability rules, expected value, variance, binomial and geometric models, normal distributions, probability density, cumulative distributions, and model interpretation.

Skills covered

  • Checking probability distributions, complements, independence, and mutually exclusive events
  • Computing expected value and variance and interpreting long-run behavior and spread
  • Recognizing binomial conditions, parameters, expected values, and variances
  • Using geometric, continuous, density, cumulative, and normal distribution ideas
  • Standardizing values with z-scores and evaluating assumptions and model limitations

How to use these practice tests

First decide whether the random variable is a count or a measurement. Then identify the distribution and parameters, check its conditions, and interpret the probability or expected value in context.

For more Grade 12 Math practice, return to the Grade 12 Math category.

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5 Tests
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1. Test

Grade 12 Probability Distributions Practice Tests

Practice Grade 12 Math questions about discrete and continuous random variables, expected value, variance, binomial and geometric distributions, normal distributions, probability density, and sampling models.

Choose the best answer. Identify the random-variable type and distribution, check parameters and conditions, then calculate or interpret the requested probability.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the sum of all probabilities in a discrete probability distribution?

Please select an answer first.

Correct answer: A

The correct answer is 1.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Every possible outcome is included exactly once, so the probabilities sum to 1.
  3. Check the probability and interpretation: The correct answer is 1.

Every possible outcome is included exactly once, so the probabilities sum to 1.

2. QuestionMultiple choice

A fair die is rolled. What is P(rolling a 4)?

Please select an answer first.

Correct answer: B

The correct answer is 16\frac{1}{6}.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: There is one favorable face among six equally likely faces.
  3. Check the probability and interpretation: The correct answer is 16\frac{1}{6}.

There is one favorable face among six equally likely faces.

3. QuestionMultiple choice

What is the expected value of a fair six-sided die?

Please select an answer first.

Correct answer: C

The correct answer is 3.5.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: The mean of 1,2,3,4,5,6 is 21/6=3.5.
  3. Check the probability and interpretation: The correct answer is 3.5.

The mean of 1,2,3,4,5,6 is 21/6=3.5.

4. QuestionMultiple choice

What does expected value represent?

Please select an answer first.

Correct answer: D

The correct answer is The long-run average outcome.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Expected value is the probability-weighted long-run mean.
  3. Check the probability and interpretation: The correct answer is The long-run average outcome.

Expected value is the probability-weighted long-run mean.

5. QuestionMultiple choice

If X takes values 0 and 1 with P(X=1)=0.7, what is E(X)?

Please select an answer first.

Correct answer: A

The correct answer is 0.7.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: For a Bernoulli variable, E(X)=1·0.7+0·0.3=0.7.
  3. Check the probability and interpretation: The correct answer is 0.7.

For a Bernoulli variable, E(X)=1·0.7+0·0.3=0.7.

6. QuestionMultiple choice

What is the variance of a Bernoulli variable with p=0.4?

Please select an answer first.

Correct answer: B

The correct answer is 0.24.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Bernoulli variance is p(1-p)=0.4(0.6)=0.24.
  3. Check the probability and interpretation: The correct answer is 0.24.

Bernoulli variance is p(1-p)=0.4(0.6)=0.24.

7. QuestionMultiple choice

What is the complement of event A?

Please select an answer first.

Correct answer: C

The correct answer is The event that A does not occur.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: The complement contains all outcomes outside A.
  3. Check the probability and interpretation: The correct answer is The event that A does not occur.

The complement contains all outcomes outside A.

8. QuestionMultiple choice

If P(A)=0.35, what is P(not A)?

Please select an answer first.

Correct answer: D

The correct answer is 0.65.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Use the complement rule 1-P(A)=1-0.35=0.65.
  3. Check the probability and interpretation: The correct answer is 0.65.

Use the complement rule 1-P(A)=1-0.35=0.65.

9. QuestionMultiple choice

If A and B are mutually exclusive, what is P(A and B)?

Please select an answer first.

Correct answer: A

The correct answer is 0.

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Mutually exclusive events cannot occur together.
  3. Check the probability and interpretation: The correct answer is 0.

Mutually exclusive events cannot occur together.

10. QuestionMultiple choice

If A and B are independent, which relationship is true?

Please select an answer first.

Correct answer: B

The correct answer is P(A and B)=P(A)P(B).

  1. Identify the distribution model: Determine whether the variable is discrete or continuous and identify the appropriate probability distribution and parameters.
  2. Apply the probability rule: Independence means the occurrence of one event does not change the probability of the other.
  3. Check the probability and interpretation: The correct answer is P(A and B)=P(A)P(B).

Independence means the occurrence of one event does not change the probability of the other.

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