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Quizzes > High School Quizzes > Mathematics

Compound Probability Practice Quiz

Practice Compound and Experimental Probability with Worksheets

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Interactive paper art for Compound Probability Challenge quiz engaging high school students.

A fair coin is flipped twice. What is the probability that both flips result in heads?
1/4
1/3
1/8
1/2
There are 4 equally likely outcomes when flipping two coins, and only one outcome (HH) produces two heads. Multiplying the probabilities of each independent coin flip yields 1/4.
If a die is rolled and then a coin is flipped, what is the probability of rolling a 3 and getting tails?
1/8
1/6
1/2
1/12
The probability of rolling a 3 is 1/6 and the probability of flipping tails is 1/2. Multiplying these independent probabilities gives (1/6) Ã - (1/2) = 1/12.
Two independent spinners, each with 4 equal sections numbered 1 to 4, are spun. What is the probability that both spinners land on an even number?
1/2
1/3
1/8
1/4
Each spinner has an equal chance of landing on an even number (2 out of 4 sides), so the probability per spinner is 1/2. Since the events are independent, multiplying these probabilities gives (1/2) Ã - (1/2) = 1/4.
A bag contains 3 red and 7 blue marbles. If a marble is drawn, replaced, and then a second marble is drawn, what is the probability that both marbles drawn are red?
9/10
3/10
9/100
1/10
Since the marble is replaced after the first draw, the probability of drawing a red marble remains 3/10 for each draw. Multiplying these independent probabilities gives (3/10) Ã - (3/10) = 9/100.
If you roll two standard dice, what is the probability that the sum is 7?
1/8
2/7
1/12
1/6
There are 36 possible outcomes when rolling two dice and 6 combinations yield a sum of 7. Dividing 6 by 36 simplifies to 1/6.
A bag contains 4 green and 6 yellow balls. Two balls are drawn consecutively without replacement. What is the probability that both balls are green?
2/5
4/15
1/15
2/15
The probability of drawing a green ball on the first draw is 4/10; after a green is drawn, the probability on the second draw is 3/9. Multiplying these gives 12/90, which simplifies to 2/15.
A spinner is divided into 5 equal regions, numbered 1 to 5. What is the probability of spinning a number greater than 3 on two independent spins?
2/5
1/5
4/25
1/4
Numbers greater than 3 on the spinner are 4 and 5, which gives a probability of 2/5 per spin. For two independent spins, the probability is (2/5) Ã - (2/5) = 4/25.
If two coins are tossed, what is the probability that at least one of them shows heads?
3/4
1/4
2/3
1/2
When two coins are tossed, the outcomes are HH, HT, TH, and TT. Three out of these four outcomes have at least one head, so the probability is 3/4.
A card is drawn from a deck of 52 cards and then replaced. What is the probability that both cards drawn are kings?
1/13
1/26
1/52
1/169
With replacement, the probability of drawing a king remains 4/52 for each draw. Multiplying these gives (4/52)², which simplifies to 1/169.
If a box contains 10 bulbs, 3 of which are defective, what is the probability that, when picking two bulbs without replacement, both are defective?
1/15
1/10
2/15
1/5
The probability of drawing a defective bulb first is 3/10, and after one defective bulb is removed, the second has a probability of 2/9. Multiplying these gives (3/10) Ã - (2/9) = 6/90, which simplifies to 1/15.
A fair six-sided die is rolled twice. What is the probability that the first roll is greater than 4 and the second roll is an even number?
1/3
1/9
1/6
1/8
The first roll being greater than 4 means rolling a 5 or 6, which has a probability of 2/6 (or 1/3). The second roll being even has a probability of 3/6 (or 1/2). Multiplying these gives (1/3) Ã - (1/2) = 1/6.
In a game, there is a 40% chance to win a round. If a player plays two rounds independently, what is the probability that the player wins both rounds?
40%
60%
80%
16%
Since each round is independent, the probability of winning both rounds is 0.4 Ã - 0.4 = 0.16, which is 16%.
A fair coin is tossed three times. What is the probability of getting exactly two heads?
3/8
3/4
1/2
1/4
When a coin is tossed three times, there are 8 possible outcomes. Exactly 3 of these outcomes yield exactly two heads, so the probability is 3/8.
A jar contains 5 red, 4 blue, and 6 green marbles. If you draw one marble at random, what is the probability that it is either blue or green?
1/2
3/5
2/3
1/3
There are 15 marbles in total, with 4 blue and 6 green marbles making 10 favorable outcomes. Hence, the probability is 10/15, which simplifies to 2/3.
Two standard dice are rolled. What is the probability that the product of the numbers is even?
3/4
2/3
1/2
1/4
The only way to get an odd product is if both dice show odd numbers, which has a probability of (1/2) Ã - (1/2) = 1/4. Thus, the probability of an even product is 1 - 1/4 = 3/4.
In a class, 60% of the students passed the exam on the first try, and among those who retook the exam, 50% passed. If a student is randomly selected, what is the probability that they passed the exam eventually, assuming only two attempts?
50%
60%
70%
80%
The probability of passing on the first attempt is 60%. For those who fail initially (40%), half pass on the second attempt, contributing an additional 20%. Adding these together gives 80%.
A box contains 8 red, 5 blue, and 7 green marbles. Two marbles are drawn consecutively without replacement. What is the probability that the first marble is red and the second marble is green?
8/20
28/95
14/95
7/19
The probability of drawing a red marble first is 8/20. After removing one red marble, the probability of drawing a green marble becomes 7/19. Multiplying these probabilities yields 56/380, which simplifies to 14/95.
A bag contains 10 balls numbered 1 to 10. Two balls are drawn without replacement. What is the probability that the second ball drawn is larger than the first ball?
1/2
1/10
5/9
1
For any two distinct numbers drawn without replacement, there is an equal chance that the second number is larger than the first or vice versa. This symmetry results in a probability of 1/2.
Three fair coins are tossed simultaneously. What is the probability that exactly one coin shows heads and two show tails?
1/2
1/4
2/3
3/8
When three coins are tossed, there are 8 possible outcomes. Exactly 3 outcomes yield exactly one head, so the probability is 3/8.
In an experiment, two dice are rolled. If event A is 'the sum of the dice is less than 4' and event B is 'at least one die shows a 1', what is the probability of A given B?
11/36
1/12
1/3
3/11
Event A includes the outcomes (1,1), (1,2), and (2,1), all of which satisfy event B. Dividing the probability of A (3/36) by the probability of B (11/36) yields a conditional probability of 3/11.
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Study Outcomes

  1. Apply compound probability principles to solve sequential event problems.
  2. Analyze independent and dependent events to determine outcome probabilities.
  3. Synthesize sample space models to assess complex probability scenarios.
  4. Evaluate multiple solution strategies to optimize problem-solving efficiency.
  5. Interpret interactive feedback to identify and correct calculation errors.
  6. Demonstrate increased confidence in tackling probability challenges on exams.

Compound Probability Worksheet & Cheat Sheet

  1. Understand Compound Probability - Compound probability is all about finding the chance of two or more events happening together. It builds the foundation for solving more complex probability puzzles and helps you predict outcomes with confidence. Compound Probability Definition & Examples
  2. Differentiate Independent vs Dependent Events - Independent events don't influence each other, while dependent events have outcomes that are linked. Recognizing this difference is key to picking the right formulas and avoiding calculation mistakes. Independent vs Dependent Events Explained
  3. Apply the Multiplication Rule - For independent events, you find the combined probability by multiplying their individual probabilities: P(A and B) = P(A) × P(B). This simple rule unlocks joint probability problems in a snap. Multiplication Rule Guide
  4. Use the Addition Rule for Mutually Exclusive Events - When events cannot occur at the same time, just add their probabilities: P(A or B) = P(A) + P(B). It's perfect for scenarios where only one outcome is possible. Addition Rule Demystified
  5. Handle Mutually Inclusive Events - If events can overlap, use P(A or B) = P(A) + P(B) - P(A and B). This formula subtracts the overlap so you don't double‑count shared outcomes. Inclusive Events Formula
  6. Practice with Real‑Life Scenarios - Apply these rules to fun examples like drawing special cards, rolling dice combos, or even picking colored marbles. Real‑world practice makes abstract ideas stick! Byju's Compound Probability Problems
  7. Visualize with Venn Diagrams - Venn diagrams turn overlapping events into colorful circles, making it easy to see intersections and unions. A quick sketch can save you from messy algebra. Venn Diagrams & Probability
  8. Master Conditional Probability - Conditional probability calculates an event's chance given another event has occurred: P(A|B). It's essential for dependent events and real‑life forecasts like weather or diagnosis tests. Conditional Probability Basics
  9. Use Counting Techniques - Permutations and combinations help you count possible outcomes without listing them all. These tools are indispensable when solving compound probability questions quickly. Permutations & Combinations Guide
  10. Practice Regularly - The more problems you solve, the sharper your intuition becomes! Set aside time each day for mixed drills, and watch your probability skills skyrocket. Compound Probability Practice
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