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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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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 expected value of winnings that are 10 dollars with probability 0.2 and 0 otherwise?

Please select an answer first.

Correct answer: A

The correct answer is 2 dollars.

  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: E(X)=10(0.2)+0(0.8)=2.
  3. Check the probability and interpretation: The correct answer is 2 dollars.

E(X)=10(0.2)+0(0.8)=2.

2. QuestionMultiple choice

What does variance measure in a probability distribution?

Please select an answer first.

Correct answer: B

The correct answer is Spread around the expected value.

  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: Variance is the probability-weighted squared distance from the mean.
  3. Check the probability and interpretation: The correct answer is Spread around the expected value.

Variance is the probability-weighted squared distance from the mean.

3. QuestionMultiple choice

What happens to the variance when every outcome is multiplied by 3?

Please select an answer first.

Correct answer: C

The correct answer is It is multiplied by 9.

  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: Variance scales by the square of the multiplier.
  3. Check the probability and interpretation: The correct answer is It is multiplied by 9.

Variance scales by the square of the multiplier.

4. QuestionMultiple choice

What happens to standard deviation when every outcome is multiplied by -2?

Please select an answer first.

Correct answer: D

The correct answer is It is multiplied by 2.

  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: Standard deviation scales by the absolute value of the multiplier.
  3. Check the probability and interpretation: The correct answer is It is multiplied by 2.

Standard deviation scales by the absolute value of the multiplier.

5. QuestionMultiple choice

If X and Y are independent, what is Var(X+Y)?

Please select an answer first.

Correct answer: A

The correct answer is Var(X)+Var(Y).

  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: Independent variances add.
  3. Check the probability and interpretation: The correct answer is Var(X)+Var(Y).

Independent variances add.

6. QuestionMultiple choice

What is the expected value of a sum X+Y?

Please select an answer first.

Correct answer: B

The correct answer is E(X)+E(Y).

  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 values are linear even without independence.
  3. Check the probability and interpretation: The correct answer is E(X)+E(Y).

Expected values are linear even without independence.

7. QuestionMultiple choice

What does a probability-generating model need to assign to every outcome?

Please select an answer first.

Correct answer: C

The correct answer is A probability from 0 to 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: Probabilities are between zero and one and collectively sum to one.
  3. Check the probability and interpretation: The correct answer is A probability from 0 to 1.

Probabilities are between zero and one and collectively sum to one.

8. QuestionMultiple choice

What is the probability of an impossible event?

Please select an answer first.

Correct answer: D

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: An impossible event has no outcomes in the event.
  3. Check the probability and interpretation: The correct answer is 0.

An impossible event has no outcomes in the event.

9. QuestionMultiple choice

What is the probability of a certain event?

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: A certain event contains every outcome in the sample space.
  3. Check the probability and interpretation: The correct answer is 1.

A certain event contains every outcome in the sample space.

10. QuestionMultiple choice

Why can a model be useful even if it is not perfect?

Please select an answer first.

Correct answer: B

The correct answer is It can approximate patterns and support predictions with stated assumptions.

  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: Models simplify reality while making assumptions and uncertainty explicit.
  3. Check the probability and interpretation: The correct answer is It can approximate patterns and support predictions with stated assumptions.

Models simplify reality while making assumptions and uncertainty explicit.

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