Experimental Probability

Grade 7 · statistics · 85 practice problems · read aloud

🔊 Listen to this explanation

Experimental Probability 🎯

What Is It & Why Is It Useful?

Experimental probability is the chance of an event happening based on actual experiments or data collection. Unlike theoretical probability (what we expect to happen), experimental probability shows us what actually happened when we tried it out. It's super useful for making predictions in real-world situations, like predicting the weather or a player's chance of making a free throw.

How to Calculate It: Step-by-Step

  1. Perform the experiment multiple times and record your results.
  2. Count how many times the specific event you're interested in occurred.
  3. Divide that number by the total number of trials.
  4. Simplify the fraction, or convert it to a decimal/percentage.

Formula: P(event) = (Number of times event occurred) / (Total number of trials)

Worked Examples

Example 1: Coin Toss

You flip a coin 50 times. It lands on heads 23 times. What is the experimental probability of getting heads?

Step 1: Event (Heads) occurred 23 times.
Step 2: Total trials = 50.
Step 3: P(Heads) = 23/50 = 0.46 or 46%

Example 2: Dice Roll

You roll a standard six-sided die 60 times. You roll a "5" a total of 9 times. What is P(rolling a 5)?

Step 1: Event occurred 9 times.
Step 2: Total trials = 60.
Step 3: P(5) = 9/60 = 3/20 = 0.15 or 15%

⚠️ Common Mistakes to Avoid

  • Confusing it with Theoretical Probability: Remember, experimental probability is based on what did happen in an experiment, not what you think should happen.
  • Using the Wrong Total: Always divide by the total number of trials, not the number of successful trials or the number of sides on a die.
  • Forgetting to Simplify: Always simplify your fraction to its lowest terms for the final answer.

💡 Tips & Tricks

  • Memory Aid: Think "Experimental = Evidence." It's based on the evidence you collected.
  • The more trials you do, the closer your experimental probability will usually get to the theoretical probability. This is called the Law of Large Numbers.
  • Your answer should always be a number between 0 and 1 (or 0% and 100%).

How to Practice

  • Grab a die or a coin and conduct your own experiments! Record 20, 50, or 100 trials.
  • Look for real-world data, like a basketball player's free-throw statistics, and calculate their experimental probability of making a shot.
  • Solve word problems that provide you with a data set from a fictional experiment.

Practice problems

6 of the 85, worked through step by step — try them before opening the answer.

1 (-3)² + 2 × (-4) = ?

Hint: Remember to follow the order of operations and pay attention to negative signs when squaring numbers.

Show the answer

Answer: 1

  1. Evaluate (-3)² A negative number in parentheses squared means: (-3) × (-3) = 9 So, (-3)² = 9.
  2. Evaluate 2 × (-4) Multiplying a positive number by a negative number gives a negative result: 2 × (-4) = -8.
  3. Add the results Now we have: 9 + (-8) Adding a negative is the same as subtracting: 9 - 8 = 1. Final Answer: 1

Let's solve step-by-step.

2 (-3)² + 4 × (-5) = ?

Hint: Remember to follow the order of operations and pay attention to the signs when working with negative numbers.

Show the answer

Answer: -11

  1. Evaluate (-3)² A negative number squared becomes positive: (-3) × (-3) = 9 So, (-3)² = 9.
  2. Evaluate 4 × (-5) A positive times a negative gives a negative: 4 × (-5) = -20.
  3. Add the results 9 + (-20) = 9 - 20 = -11. Final answer: -11

Let's solve step by step.

3 (-3)² + 4 × (-5) ÷ 2 = ?

Hint: Remember to follow the order of operations and pay attention to negative signs when squaring numbers.

Show the answer

Answer: -1

  1. Handle the exponent first. (-3)² means (-3) × (-3) = 9. So the expression becomes: 9 + 4 × (-5) ÷ 2
  2. Handle multiplication and division from left to right. First: 4 × (-5) = -20 Expression now: 9 + (-20) ÷ 2 Next: (-20) ÷ 2 = -10 Expression now: 9 + (-10)
  3. Do the addition. 9 + (-10) = 9 - 10 = -1 Final answer: -1

Let's solve step-by-step using the order of operations (PEMDAS/BODMAS).

4 (-3)² + 2 × (15 ÷ 3) - 7 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction.

Show the answer

Answer: 12

  1. Handle parentheses and exponents first. We have (-3)². (-3)² means (-3) × (-3) = 9. So now the expression is: 9 + 2 × (15 ÷ 3) - 7
  2. Inside the parentheses: 15 ÷ 3 = 5. Now we have: 9 + 2 × 5 - 7
  3. Multiplication comes next: 2 × 5 = 10. Now we have: 9 + 10 - 7
  4. Addition and subtraction from left to right: 9 + 10 = 19 19 - 7 = 12 Final answer: 12

Let's solve step-by-step using the order of operations (PEMDAS/BODMAS).

5 (-4)² - 3 × (18 ÷ 3 + 2) = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication/division from left to right, and finally addition/subtraction. For example, in an expression like (2)² - 1 × (10 ÷ 2 + 1), you would start with the parentheses.

Show the answer

Answer: -8

  1. Calculate inside the parentheses: 18 ÷ 3 + 2 = 6 + 2 = 8
  2. Calculate the exponent: (-4)² = 16
  3. Perform the multiplication: 3 × 8 = 24
  4. Perform the subtraction: 16 - 24 = -8

The answer is -8.

6 (-4)² - 3 × (18 ÷ 6 + 2) = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication/division from left to right, and finally addition/subtraction from left to right.

Show the answer

Answer: 1

  1. Solve inside the parentheses: 18 ÷ 6 + 2 = 3 + 2 = 5
  2. Calculate the exponent: (-4)² = 16
  3. Perform the multiplication: 3 × 5 = 15
  4. Complete the subtraction: 16 - 15 = 1
  5. The final answer is 1.
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