Probability Concepts

Grade 7 · statistics · 74 practice problems · read aloud

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📊 Probability Concepts

What is Probability?

Probability is a measure of how likely an event is to happen. We use it to predict chances in games, weather forecasts, and everyday decisions. It's always a number between 0 (impossible) and 1 (certain).

How to Calculate Probability

  1. Identify the total number of possible outcomes.
  2. Identify the number of favorable outcomes (what you want to happen).
  3. Divide: Probability = (Favorable Outcomes) / (Total Possible Outcomes).
  4. Simplify the fraction or convert it to a decimal/percentage.

Visual Examples

Example 1: Rolling a Die

What's the probability of rolling a 4 on a fair 6-sided die?

  • Favorable outcomes: 1 (just the number 4)
  • Total outcomes: 6 (numbers 1 through 6)
  • P(4) = 1/6

Example 2: Picking a Marble

A bag has 3 red, 2 blue, and 5 green marbles. What is P(picking green)?

  • Favorable outcomes: 5 green marbles
  • Total outcomes: 3 + 2 + 5 = 10 marbles total
  • P(green) = 5/10 = 1/2

🚨 Common Mistakes

  • Confusing "favorable" with "total": Always double-check which number goes on top in the fraction.
  • Forgetting to simplify: A probability of 2/8 should be simplified to 1/4.
  • Probabilities greater than 1: If your answer is greater than 1, you've swapped the numbers in your fraction!

💡 Tips & Tricks

  • Impossible = 0, Certain = 1: All probabilities live between these two numbers.
  • Make a list: For tricky problems, list all possible outcomes to avoid missing any.
  • Check your answer: Does your probability make sense? Is it likely or unlikely?

Practice Suggestions

To get better at probability:

  • Use a deck of cards or dice to create your own problems.
  • Look for probability in real life (e.g., chance of rain, game shows).
  • Practice with spinners, coin flips, and simple scenarios first.

Practice problems

6 of the 74, worked through step by step — try them before opening the answer.

1 P(rolling a 3 on a fair six-sided die) = ?

Hint: Consider how many equally likely outcomes exist and how many of them match the desired event.

Show the answer

Answer: 1/6

  1. Understand the problem. We are asked for the probability of rolling a 3 on a fair six-sided die.
  2. Identify the total number of possible outcomes. A fair six-sided die has 6 faces, numbered 1, 2, 3, 4, 5, and 6. Therefore, the total number of possible outcomes when you roll the die is 6.
  3. Identify the number of favorable outcomes. A "favorable outcome" is the one we are looking for, which is rolling a 3. Only one face of the die shows the number 3. Therefore, the number of favorable outcomes is 1.
  4. Apply the probability formula. The probability of an event is given by: Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
  5. Substitute the numbers into the formula. Number of favorable outcomes = 1 Total number of possible outcomes = 6 So, Probability = 1 / 6
  6. State the final answer. The probability of rolling a 3 is 1/6.

2 P(rolling a 3 or 4 on a fair six-sided die) = ?

Hint: Consider how many outcomes are favorable compared to the total possible outcomes.

Show the answer

Answer: 1/3

  1. Understand the problem. We are rolling a fair six-sided die. The faces are numbered 1, 2, 3, 4, 5, and 6. We want the probability of rolling a 3 OR a 4.
  2. Recall the basic probability formula. For an event, Probability = (Number of favorable outcomes) / (Total number of possible outcomes).
  3. Identify the total number of possible outcomes. Since the die is fair and has six sides, there are 6 possible outcomes (1, 2, 3, 4, 5, 6). So, total outcomes = 6.
  4. Identify the number of favorable outcomes. The favorable outcomes are the outcomes we want: rolling a 3 or rolling a 4. This gives us 2 favorable outcomes (3 and 4).
  5. Apply the probability formula. Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 2 / 6.
  6. Simplify the fraction. The fraction 2/6 can be simplified by dividing the numerator and denominator by 2. 2 divided by 2 is 1, and 6 divided by 2 is 3. So, 2/6 simplifies to 1/3.
  7. State the final answer. Therefore, the probability of rolling a 3 or a 4 is 1/3.

3 P(rolling a 3 or 5 on a fair six-sided die) = ?

Hint: Consider how many outcomes satisfy the condition compared to the total possible outcomes.

Show the answer

Answer: 1/3

  1. Understand the problem. We have a fair six-sided die. The possible outcomes when rolling it are: 1, 2, 3, 4, 5, 6. We want the probability of rolling a 3 OR a 5.
  2. Recall the formula for probability. Probability = (Number of favorable outcomes) / (Total number of possible outcomes).
  3. Identify the total number of possible outcomes. Since the die has six sides, there are 6 possible outcomes. So, total outcomes = 6.
  4. Identify the number of favorable outcomes. Favorable outcomes are the outcomes we want, which are rolling a 3 OR rolling a 5. - Rolling a 3 is one favorable outcome. - Rolling a 5 is another favorable outcome. So, total favorable outcomes = 1 + 1 = 2.
  5. Calculate the probability. Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 2 / 6.
  6. Simplify the fraction. The fraction 2/6 can be simplified by dividing the numerator and denominator by 2. 2 divided by 2 is 1. 6 divided by 2 is 3. So, 2/6 simplifies to 1/3.
  7. State the final answer. Therefore, the probability of rolling a 3 or a 5 is 1/3.

4 P(rolling a 2 or 4 on a fair six-sided die) = ?

Hint: Consider how many favorable outcomes there are compared to the total possible outcomes.

Show the answer

Answer: 1/3

  1. Identify the total number of possible outcomes on a fair six-sided die: 6
  2. Identify the favorable outcomes (rolling a 2 or 4): 2 outcomes
  3. Calculate the probability by dividing favorable outcomes by total outcomes: 2/6
  4. Simplify the fraction: 2/6 = 1/3

The answer is 1/3.

5 P(rolling a 1 or 6 on a fair six-sided die) = ?

Hint: Consider how many favorable outcomes there are compared to the total possible outcomes when rolling a die.

Show the answer

Answer: 1/3

  1. Identify the total number of possible outcomes when rolling a fair six-sided die. There are 6 possible outcomes (1, 2, 3, 4, 5, 6).
  2. Identify the number of favorable outcomes (rolling a 1 or a 6). There are 2 favorable outcomes.
  3. Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 2/6.
  4. Simplify the fraction 2/6 by dividing the numerator and denominator by 2: 2/6 = 1/3.

The answer is 1/3.

6 P(rolling a 1 or 5 on a fair six-sided die) = ?

Hint: Consider how many favorable outcomes exist out of all possible outcomes when rolling a standard die.

Show the answer

Answer: 1/3

  1. A fair six-sided die has outcomes: 1, 2, 3, 4, 5, 6. So, total possible outcomes = 6.
  2. Favorable outcomes for rolling a 1 or 5 are: 1, 5. So, number of favorable outcomes = 2.
  3. Probability = (Number of favorable outcomes) / (Total possible outcomes) = 2/6.
  4. Simplify the fraction: 2/6 = 1/3.

The answer is 1/3.

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