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Quizzes > High School Quizzes > Mathematics

AP Statistics Probability Test Practice Quiz

Ace your probability skills with practice tests

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

What is the probability of getting heads when flipping a fair coin?
1/3
1/2
0
1
A fair coin has two equally likely outcomes: heads or tails. Therefore, the probability of getting heads is 1 divided by 2, which equals 1/2.
If a six-sided die is rolled, what is the probability of rolling a number greater than 4?
1/6
1/2
1/3
2/3
The numbers greater than 4 on a six-sided die are 5 and 6. Thus, there are 2 favorable outcomes out of 6, which simplifies to a probability of 1/3.
What does the term 'sample space' represent in probability?
A measure of central tendency
The set of all possible outcomes
A summary of collected data
A single outcome
The sample space is defined as the set of all possible outcomes in a probability experiment. Knowing the sample space is essential for calculating probabilities accurately.
In a random experiment, what is considered a 'favorable' outcome?
An outcome that satisfies the event's condition
The outcome that happens most frequently
Any possible outcome
An outcome that is unexpected
A favorable outcome is one that meets the specific conditions of the event being analyzed. It is used in the calculation of the probability by comparing it to the total number of outcomes.
What is the complement of an event A in probability?
An outcome that occurs most frequently
The same as event A
All outcomes not in event A
An outcome that rarely occurs
The complement of an event A comprises all outcomes that are not included in A. This concept is pivotal because the probabilities of an event and its complement sum to 1.
When two fair coins are tossed simultaneously, what is the probability of getting exactly one head?
1/4
3/4
1
1/2
There are 4 possible outcomes when two coins are tossed. Since exactly one head occurs in 2 out of these 4 outcomes, the probability is 2/4, which simplifies to 1/2.
A bag contains 5 red and 3 blue marbles. What is the probability of drawing a blue marble randomly?
5/8
3/5
3/8
1/2
The total number of marbles is 5 + 3 = 8. Since there are 3 blue marbles, the probability of drawing one is 3/8.
In a standard deck of 52 cards, what is the probability of drawing a heart?
1/3
1/2
1/13
1/4
There are 13 hearts in a deck of 52 cards. Dividing 13 by 52 gives a probability of 1/4.
Which probability rule states that the probability of the complement of an event equals 1 minus the probability of the event?
Addition Rule
Complement Rule
Multiplication Rule
Inclusion-Exclusion Principle
The Complement Rule is used to determine the probability of an event not occurring by subtracting the event's probability from 1. This rule is fundamental in simplifying many probability problems.
For two independent events A and B, what is the probability that both events occur?
P(A) × P(B)
P(A) / P(B)
P(A) + P(B)
P(A) - P(B)
When events are independent, the probability that both occur is the product of their individual probabilities. This multiplication rule is a key principle in probability theory.
A spinner is divided into 8 equal regions numbered 1 through 8. What is the probability of landing on an even number?
1/2
1/4
3/8
1/8
There are four even numbers (2, 4, 6, 8) out of 8 possible outcomes on the spinner. Therefore, the probability of landing on an even number is 4/8, which simplifies to 1/2.
When drawing two cards from a deck without replacement, how are the events affected?
The events become dependent
The total number of outcomes increases
The events remain independent
There is no impact on the probabilities
Drawing cards without replacement means that the outcome of the first draw influences the second draw. This dependency alters the probabilities compared to independent events.
When a die is rolled once, which number is most likely to appear?
All outcomes are equally likely
None of the above
One
Six
A fair die has six faces and each face has an equal chance of occurring. Therefore, no single number is more likely than the others; all outcomes are equally likely.
What does it mean for events to be mutually exclusive?
They always occur together
They cannot occur at the same time
Their probabilities add up to more than 1
They are independent events
Mutually exclusive events are defined as events that cannot occur simultaneously. This concept is used to ensure that when calculating probabilities, overlapping events are not counted multiple times.
A fair coin is flipped 3 times. What is the probability of obtaining exactly two heads?
3/8
1/2
1/4
2/3
When a coin is flipped 3 times, there are 8 possible outcomes. Exactly two heads occur in 3 of those outcomes, so the probability is 3/8.
A jar contains 4 red, 5 blue, and 6 green candies. If two candies are drawn without replacement, what is the probability that both are blue?
2/15
1/7
4/21
2/21
The probability of drawing a blue candy first is 5/15. Once a blue candy is removed, the probability of drawing another blue candy is 4/14. Multiplying these yields (5/15) × (4/14) = 2/21.
In a group of 10 students, 4 are left-handed. What is the probability of randomly selecting two left-handed students consecutively without replacement?
2/9
1/5
2/15
4/15
The probability that the first student selected is left-handed is 4/10. After removing one left-handed student, the probability that the second is left-handed becomes 3/9. Multiplying these probabilities gives (4/10) × (3/9) = 2/15.
If the probability that a student passes an exam is 0.8, what is the probability that exactly 3 out of 5 students pass, assuming independent events?
0.8
0.32
0.2048
0.4096
This problem uses the binomial probability formula: P = C(5,3) × (0.8)^3 × (0.2)^2. Calculating this gives 10 × 0.512 × 0.04 = 0.2048.
A bag contains 7 balls numbered 1 through 7. If two balls are drawn sequentially without replacement, what is the probability that the second ball is greater than the first?
6/7
1/7
1/3
1/2
Any two distinct numbers drawn can be arranged in two orders, one of which will have the second number greater than the first. Therefore, the probability is 1/2.
In a lottery where 6 numbers are drawn from a pool of 49, how many different combinations are possible?
13,983,816
10,000,000
14,000,000
6,497,400
The total number of combinations is calculated using the combination formula C(49,6). This computes to 13,983,816, representing the number of ways to choose 6 numbers from 49 when order does not matter.
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Study Outcomes

  1. Analyze real-world probability scenarios to determine accurate outcomes.
  2. Apply fundamental probability rules to solve challenging problems.
  3. Interpret statistical data to assess event likelihoods.
  4. Evaluate real-life situations using probability concepts effectively.
  5. Synthesize information from multiple sources to build confident solutions for AP exam challenges.

AP Stats Probability Practice Test Cheat Sheet

  1. Understanding Probability Basics - Grasp the fundamentals like experiments, sample spaces, and events in a snap. Imagine rolling a die: the sample space is {1, 2, 3, 4, 5, 6}, and each roll is an event. This solid foundation will be your prob‑hero cape as you tackle more complex probability puzzles! CliffsNotes - Probability Basics
  2. Complement Rule - Learn that the chance of an event not happening is just 1 minus the chance it does. So if the probability of rain is 0.35, the probability of a dry day is 1 - 0.35 = 0.65. It's a simple trick that instantly doubles your probability superpowers! Varsity Tutors - Complement Rule
  3. Addition Rule for Mutually Exclusive Events - Get ready to add up your chances when events can't crash together. If two events can't happen at the same time, simply sum their probabilities. For example, drawing a heart or a spade from a deck is P(Heart) + P(Spade). Fiveable - Mutually Exclusive Events
  4. Addition Rule for Non‑Mutually Exclusive Events - When events can team up, don't forget to subtract the overlap! The probability of either event is P(A) + P(B) - P(A and B). For instance, pulling a heart or a king from a deck: P(Heart) + P(King) - P(Heart and King). Fiveable - Non‑Mutually Exclusive Events
  5. Multiplication Rule for Independent Events - For events that don't affect each other, multiply their individual probabilities to find the joint chance. Flipping two heads in a row is just P(Head) × P(Head). It's the math equivalent of "what are the odds?" x "what are the odds?" Fiveable - Independent Events
  6. Multiplication Rule for Dependent Events - When events are linked, use conditional probability: P(A) × P(B|A). Picture drawing two aces in a row without replacement: P(Ace on first draw) × P(Ace on second draw | first was an Ace). Fiveable - Dependent Events
  7. Conditional Probability - Zero in on the probability of an event given that another event has already occurred. It's calculated as P(A|B) = P(A and B) / P(B). For example, the chance of drawing a king given that you already pulled a face card is P(King|Face Card). Fiveable - Conditional Probability
  8. Law of Total Probability - Sum up every pathway to an event by partitioning your sample space. P(A) = Σ P(A|Bᵢ) × P(Bᵢ). It's like mapping all possible routes on a treasure hunt and adding up each path's odds! Fiveable - Law of Total Probability
  9. Bayes' Theorem - Flip your conditional probabilities around to update beliefs with new evidence. P(A|B) = [P(B|A) × P(A)] / P(B). Perfect for detective work, medical testing, or nailing those "what if" scenarios under uncertainty! Fiveable - Bayes' Theorem
  10. Permutations and Combinations - Know when order matters (permutations) versus when it doesn't (combinations). Use nPr = n! / (n - r)! for ordered arrangements and nCr = n! / [r!(n - r)!] for unordered selections. These are your go‑to tools for counting everything from passwords to pizza toppings! Fiveable - Permutations & Combinations
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