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Quizzes > High School Quizzes > Mathematics

AP Stats Probability Practice Quiz

Sharpen your skills with focused practice questions

Difficulty: Moderate
Grade: Grade 12
Study OutcomesCheat Sheet
Colorful paper art promoting AP Stats Probability Quest trivia for high school students

If you flip a fair coin, what is the probability of landing heads?
0.5
0.25
1
0
A fair coin has two equally likely outcomes: heads or tails, so the probability for heads is 1 out of 2. This makes the correct answer 0.5.
In a standard deck of 52 cards, what is the probability of drawing an Ace?
12/52
4/52
13/52
1/52
There are 4 Aces in a 52-card deck, so the probability is 4/52. This fraction simplifies to 1/13, but 4/52 is the provided correct form.
What is the complement of an event?
The event that does not happen
The event that always occurs
The probability of the event
An unrelated event
The complement of an event consists of all outcomes that do not belong to the event. Hence, it is correctly defined as the event that does not happen.
If an event has a probability of 1, what does that imply?
The event is unlikely
The event is impossible
The event is random
The event is certain
A probability of 1 indicates the event is guaranteed to occur. Such an event is described as certain.
What is a sample space in probability?
A subset of outcomes
A probability model
The set of all possible outcomes
An event with high probability
The sample space comprises all possible outcomes of an experiment. This complete set is fundamental to defining probabilities.
A bag contains 3 red, 4 blue, and 5 green marbles. What is the probability of drawing a blue marble at random?
4/12
5/12
3/12
7/12
The bag has a total of 12 marbles and 4 of them are blue. Therefore, the probability of drawing a blue marble is 4/12, which simplifies to 1/3.
If two independent events A and B have probabilities 0.3 and 0.5 respectively, what is the probability that both occur?
0.5
0.8
0.15
0.3
For independent events the probability of both occurring is the product of their individual probabilities: 0.3 * 0.5 equals 0.15. This application of the multiplication rule confirms the answer.
How many outcomes are there when rolling two six-sided dice?
12
42
6
36
Each die has 6 outcomes, and when rolling two dice, the outcomes multiply: 6 x 6 equals 36. This is the total number of possible outcomes.
Which probability rule applies when calculating the probability of the union of two mutually exclusive events?
Complement rule
Addition rule with subtraction
Multiplication rule
Simple addition
For mutually exclusive events, the events cannot occur simultaneously, so their probabilities are added directly. No overlap exists, making simple addition the correct rule.
A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability of landing on a prime number?
1/8
1/4
3/4
1/2
The prime numbers from 1 to 8 are 2, 3, 5, and 7, which gives 4 favorable outcomes. Dividing by the 8 possible outcomes, the probability is 4/8 or 1/2.
When drawing two cards from a deck without replacement, what type of events are these?
Dependent events
Complementary events
Mutually exclusive events
Independent events
Drawing cards without replacement alters the composition of the deck for the second draw. This dependency makes the events dependent.
In a probability distribution for a discrete random variable, what must the sum of all probabilities equal?
1
It can vary
0.5
0
The defining property of any discrete probability distribution is that the sum of all individual probabilities must equal 1. This represents the certainty that one of the outcomes will occur.
Using the combination formula, how many ways can you choose 3 items from a set of 7 distinct items?
7
21
35
42
The number of ways to choose 3 items from 7 is computed using 7C3, which equals 35. This calculation follows the combination formula nCk = n! / (k!(n-k)!).
Which of the following best describes independent events?
Events that cannot occur at the same time
Events whose occurrence affects each other
Events that are complementary
Events with no influence on each other
Independent events are characterized by the fact that the occurrence of one does not affect the probability of the other occurring. This lack of influence is the key attribute of independent events.
What term describes the measure of the likelihood of an outcome in a probability experiment?
Regression
Variance
Probability
Statistical significance
Probability is the measure used to describe how likely an outcome is in any probability experiment. It quantifies the chance of occurrence for a particular event.
A factory produces 60% of its products from Machine A and 40% from Machine B. Machine A produces 2% defective products and Machine B produces 5% defective products. If a randomly selected product is defective, what is the probability it was produced by Machine B?
0.625
0.8
0.375
0.5
Bayes' theorem allows us to determine the probability that a defective product was produced by Machine B. The calculation (0.40*0.05) / (0.60*0.02 + 0.40*0.05) results in 0.625.
A fair six-sided die is rolled three times. What is the probability that exactly two of the rolls result in a 4?
5/36
5/72
1/6
1/12
This problem fits a binomial probability model where n=3 trials, k=2 successes, probability of a '4' is 1/6, and failure is 5/6. The calculation 3*(1/6)^2*(5/6) simplifies to 5/72.
In an experiment, a random variable X has a probability mass function given by P(X=x) = c*x for x = 1, 2, 3, 4. What is the value of c?
0.1
0.2
0.05
0.25
The sum of the probabilities must equal 1, so c*(1+2+3+4) = 10c = 1. Solving for c yields c = 0.1.
A box contains 5 defective and 15 non-defective bulbs. If three bulbs are drawn at random without replacement, what is the probability that exactly one is defective?
5/12
35/76
105/380
7/15
The probability is calculated by selecting 1 defective bulb (from 5) and 2 non‑defective bulbs (from 15) divided by the total ways to choose 3 from 20. This gives (5C1 * 15C2) / 20C3, which simplifies to 35/76.
A continuous random variable X is uniformly distributed between 2 and 10. What is the probability that X is less than 5?
0.625
0.375
0.25
0.5
For a uniform distribution, the probability is proportional to the length of the interval. The portion of the interval from 2 to 5 is 3 units long out of a total of 8 units, yielding a probability of 3/8 or 0.375.
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Study Outcomes

  1. Understand fundamental probability concepts and terminology.
  2. Analyze random experiments to identify outcomes and compute probabilities.
  3. Apply theoretical probability models to solve real-world problems.
  4. Evaluate the impact of independent and dependent events on probability calculations.
  5. Synthesize key AP Statistics concepts to enhance problem-solving strategies.

AP Stats Probability Cheat Sheet

  1. Addition Rule - Think of this as combining event buckets. For events that can't happen together (mutually exclusive), simply add their probabilities. If they can overlap, subtract the intersection so you don't double‑count shared outcomes. Fiveable's Probability Rules
  2. Multiplication Rule - This rule is all about joint occurrences. For independent events, multiply their probabilities directly. When events are dependent, factor in conditional probability by using P(A) × P(B|A) to capture the updated chance. Fiveable's Probability Rules
  3. Conditional Probability - Here you're zooming in on the chance of A given that B already happened. Calculate it by dividing the probability of both A and B occurring by the probability of B. This lets you update your expectations based on new information. Fiveable's Probability Rules
  4. Bayes' Theorem - Bayes lets you flip probabilities when you get fresh evidence. Use P(A|B) = [P(B|A) × P(A)] / P(B) to revise your belief in A after observing B. It's a powerful tool for real‑world decision making and diagnostics. Fiveable's Probability Rules
  5. Complementary Events - Sometimes it's easier to calculate what won't happen. The probability of the complement (A′) is just 1 minus the probability of A. This trick simplifies problems like "at least one" or "none of the above." Fiveable's Probability Rules
  6. Expected Value - Think of this as the long‑run average outcome. Multiply each possible value by its probability and sum them up to get E(X). It tells you what to expect on average if you repeat the experiment many times. Statistics How To: AP Formulas
  7. Variance of a Random Variable - Variance measures how spread out your outcomes are. Calculate Σ[(xᵢ − μ)² × P(xᵢ)] to see how each value deviates from the mean. A larger variance means more risk or variability in your results. Statistics How To: AP Formulas
  8. Binomial Probability - Use this when you have a fixed number of trials and each is a success/fail. The formula P(X = x) = nCx × pˣ × (1−p)❿❻ˣ gives the chance of exactly x successes. It's perfect for things like coin flips or quality‑control checks. Statistics How To: AP Formulas
  9. Permutations & Combinations - Permutations (nPr) count ordered arrangements: nPr = n!/(n−r)!. Combinations (nCr) count unordered selections: nCr = n!/[r!(n−r)!]. Pick permutations when order matters, combinations when it doesn't. Fiveable's Probability Rules
  10. Law of Total Probability - Break a complex event into simpler, exhaustive cases B₝…Bₙ. Then sum P(A|Bᵢ)×P(Bᵢ) across all i to get P(A). It's a handy way to combine different scenarios. Fiveable's Probability Rules
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