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Quizzes > High School Quizzes > Mathematics

Probability Practice Test for Unit Success

Sharpen your probability skills with interactive problems

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Probability Power Play, a dynamic high school quiz.

What is the probability of getting heads when flipping a fair coin?
1/2
1/3
1/4
1/6
A fair coin has two equally likely outcomes: heads or tails. Therefore, the chance of getting heads is 1/2, while the other options do not reflect the correct ratio.
What is the probability of rolling a 3 on a fair six-sided die?
1/6
1/3
1/2
1/4
A six-sided die has six outcomes, and only one outcome is a 3. Hence, the probability of rolling a 3 is 1/6.
In a bag containing 2 red and 3 blue marbles, what is the probability of drawing a red marble?
2/5
3/5
1/2
2/3
There are 2 favorable outcomes (red marbles) out of 5 total marbles. Therefore, the probability of drawing a red marble is 2/5.
Which of the following is an impossible probability value?
1.2
0.5
0
1
Probability values must be between 0 and 1 inclusive. A value of 1.2 falls outside this range and is therefore impossible.
If an event has a probability of 0, what does that indicate?
It is impossible
It is certain
It is likely
It is random
A probability of 0 means that the event cannot occur. This is in contrast with events that have a chance of happening.
What is the probability of getting two heads in two consecutive flips of a fair coin?
1/4
1/2
1/8
1/16
Since each coin flip has a probability of 1/2 for heads, two consecutive heads have a probability of (1/2) x (1/2) = 1/4. The other options do not reflect the multiplication rule for independent events.
A bag contains 4 green balls and 6 yellow balls. What is the probability of drawing a green ball?
2/5
3/5
1/2
4/5
There are 4 green balls out of a total of 10 balls, making the probability 4/10, which simplifies to 2/5. The other answers do not represent the correct simplified fraction.
When two dice are rolled, what is the probability that the sum is 7?
1/6
1/4
5/36
7/36
There are 6 combinations to achieve a sum of 7 out of 36 total outcomes when rolling two dice. This simplifies to 1/6, making it the correct answer.
Which scenario describes independent events?
Flipping a coin and rolling a die
Drawing two cards from a deck without replacement
Selecting a marble and not replacing it
Rolling the same die twice with the outcome of the first affecting the second
Flipping a coin and rolling a die are independent events because the outcome of one does not affect the outcome of the other. The other scenarios involve dependency due to changes in composition or sequential impacts.
What is the complement of an event with a probability of 0.3?
0.7
0.3
1.3
0.5
The complement of an event is calculated as 1 minus the probability of the event. Therefore, 1 - 0.3 equals 0.7, making that the correct answer.
A spinner is divided into 4 equal sections numbered 1 through 4. What is the probability of spinning a number greater than 2?
1/2
1/4
3/4
2/3
Only the numbers 3 and 4 are greater than 2, which gives 2 favorable outcomes out of 4 total. This simplifies to a probability of 1/2.
Which scenario best describes mutually exclusive events?
Tossing a coin where it lands on heads or tails
Rolling a die where the result can be even or less than 5
Choosing a card that is both red and a queen
Drawing a card that is either a heart or a king
Mutually exclusive events cannot occur at the same time. In a coin toss, the outcome is either heads or tails, which perfectly fits this definition.
If an event can occur in 8 different ways out of 32 possible outcomes, what is its probability?
1/4
1/3
1/8
2/3
Dividing the number of favorable outcomes (8) by the total outcomes (32) yields 8/32, which simplifies to 1/4. This is the correct probability.
When a fair six-sided die is rolled, what is the probability of rolling an even number?
1/2
1/3
2/3
1/4
There are three even numbers (2, 4, and 6) on a six-sided die. Thus, the probability of rolling an even number is 3/6, which simplifies to 1/2.
How do you calculate the probability of two independent events both occurring?
By multiplying their individual probabilities
By adding their probabilities
By subtracting the probability of one from the other
By dividing one probability by the total number of events
For independent events, the correct method is to multiply the probabilities of each event. The other methods do not correctly apply to the multiplication rule governing independent events.
If a box contains 5 defective and 15 non-defective bulbs, and two bulbs are drawn without replacement, what is the probability that both are defective?
1/19
1/16
1/10
1/23
The probability of drawing a defective bulb first is 5/20, and after one defective is drawn, the probability for the second is 4/19. Multiplying these gives (5/20) x (4/19) = 1/19.
A jar contains 3 red, 4 blue, and 5 green marbles. What is the probability of picking a marble that is not blue?
2/3
1/2
1/3
3/4
There are 12 marbles in total, and the non-blue marbles total 8 (3 red + 5 green). Thus, the probability of not picking a blue marble is 8/12, which simplifies to 2/3.
When rolling two standard dice, what is the probability of rolling doubles (both dice show the same number)?
1/6
1/3
1/12
1/9
Doubles occur when both dice show the same number, and there are 6 such outcomes out of 36 total possibilities, which simplifies to a probability of 1/6.
A fair coin is tossed 3 times. What is the probability of getting exactly two heads?
3/8
1/2
1/4
2/3
There are 8 possible outcomes when tossing a coin 3 times, and exactly two heads occur in 3 different sequences. This gives a probability of 3/8.
A bag contains 10 balls numbered 1 to 10. What is the probability that a randomly selected ball is a prime number?
2/5
1/2
3/10
1/5
Between 1 and 10, the prime numbers are 2, 3, 5, and 7, making 4 favorable outcomes out of 10. This probability simplifies to 2/5.
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Study Outcomes

  1. Understand key probability concepts such as outcomes, events, and sample spaces.
  2. Apply counting principles to determine the number of possible outcomes.
  3. Analyze problems to calculate the likelihood of simple events.
  4. Evaluate the difference between theoretical and experimental probabilities.
  5. Solve problems involving independent and mutually exclusive events.

Probability Unit Test Cheat Sheet

  1. Probability Formula - The probability formula finds chances by dividing the number of favorable outcomes by all possible outcomes. It's the cornerstone for everything from dice rolls to lottery picks. Try practicing with coins, dice, or shuffled cards to see it work in real time! BYJU's Probability Formulas
  2. Addition Rule - The addition rule calculates the probability of either event A or B happening by adding their individual probabilities and subtracting any overlap. This helps avoid double-counting when events can occur together. Use Venn diagrams to visualize and master this concept faster. Addition Rule - GeeksforGeeks
  3. Multiplication Rule - When two events are independent, their joint probability equals the product of their separate probabilities. This rule lets you compute the chance of two or more events happening in a row. Practice by rolling multiple dice or drawing cards one after another. Multiplication Rule - GeeksforGeeks
  4. Conditional Probability - Conditional probability measures the chance of event A given that event B has already occurred. It's essential for scenarios where events influence each other, like drawing cards without replacement. Drawing event trees can make these problems a breeze! Conditional Probability - Core Standards
  5. Complementary Events - Complementary events are pairs where one event's chance is 1 minus the other's probability. If the chance of rain is 0.7, the chance of no rain is 0.3. Always check if working with complements simplifies your calculations. Complementary Events - BYJU's
  6. Mutually Exclusive vs Independent - Mutually exclusive events cannot happen at the same time, while independent events don't affect each other's probabilities. Recognizing the difference is key to picking the right rule. Imagine flipping a coin and rolling a die to see these concepts in action. Mutually Exclusive & Independent - Core Standards
  7. Permutations & Combinations - Permutations count outcomes where order matters, such as seating arrangements, while combinations ignore order, like choosing team members. These tools help you count possible outcomes quickly. Try different problems to get comfortable with both methods. Permutations & Combinations - Math is Fun
  8. Probability Distributions - A probability distribution lists all possible outcomes and their associated probabilities. Understanding distributions makes it easier to predict how a random variable behaves over many trials. Plotting histograms can give you a visual edge on spotting patterns. Probability Distributions - Math is Fun
  9. Bayes' Theorem - Bayes' Theorem updates the probability of an event based on new evidence or information. It's a powerful tool for fields like medical testing and spam filtering. Practice with real-world examples to see Bayesian thinking in action. Bayes' Theorem - GeeksforGeeks
  10. Real-Life Scenarios - Applying probability to games, weather forecasts, or sports stats makes learning fun and practical. Real-world practice reinforces theory and boosts your problem-solving skills. Challenge yourself with daily examples to master these concepts for exams and beyond. Probability in Real Life - BYJU's
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