Year 9 Maths: Experimental Probability

What is Experimental Probability?

Experimental probability is a way to find out how likely something is to happen based on actual experiments or trials. Instead of just guessing, we conduct experiments and record the results. This helps us understand the probability of an event more accurately.

How Do We Calculate Experimental Probability?

To calculate experimental probability, we use this simple formula:

Example:

Imagine we want to find out the probability of rolling a 4 on a six-sided die. We roll the die 30 times and get a 4 on 6 of those rolls.

Using our formula:

• Number of times we rolled a 4 = 6
• Total rolls = 30

So, the experimental probability of rolling a 4 is:

This means there is a 20% chance (or 1 in 5) of rolling a 4 based on our experiment.

Key Rules of Experimental Probability

1. Conduct Many Trials: The more times you conduct an experiment, the more reliable your probability will be.
2. Keep Accurate Records: Always write down your results clearly. This helps you calculate the probability accurately.
3. Understand Variability: Sometimes, your experimental results may not match the theoretical probability. That’s okay! It happens because of chance.

Tips and Tricks

• Use Simple Experiments: Start with easy experiments like flipping coins or rolling dice.
• Organise Your Data: Use charts or tables to keep track of your results. Visual aids can help you see patterns.
• Discuss Results: Talk about your findings with classmates. This can help you understand different perspectives on probability.

Example Scenario

Let’s say you want to find out how often it rains on a Saturday. You keep a record of the weather for 12 Saturdays:

• It rained 4 times.

To find the experimental probability of rain on a Saturday:

This means there is about a 33% chance it will rain on a Saturday based on your data.

Questions on Experimental Probability

Easy Level Questions

1. If you flip a coin 10 times and get 6 heads, what is the experimental probability of getting heads?
2. You roll a die 12 times and get a 3 three times. What is the experimental probability of rolling a 3?
3. You draw a card from a deck 20 times and get an Ace 2 times. What is the experimental probability of drawing an Ace?
4. If a spinner lands on red 5 times out of 15 spins, what is the experimental probability of landing on red?
5. You count the number of times it snows in January over 5 years. If it snowed 3 times, what is the experimental probability of snow?
6. A bag contains 10 marbles (3 red, 7 blue). If you draw a marble 5 times and get 2 red marbles, what is the experimental probability of drawing a red marble?
7. You toss a coin 20 times and get tails 8 times. What is the experimental probability of getting tails?
8. If you roll a die 24 times and get a 5 four times, what is the experimental probability of rolling a 5?
9. You survey 30 friends about their favourite colour and find 10 like blue. What is the experimental probability of choosing someone who likes blue?
10. A student tests a new video game for 40 hours and wins 12 times. What is the experimental probability of winning?

Medium Level Questions

1. If you roll a die 60 times and get a 2 eleven times, what is the experimental probability of rolling a 2?
2. You flip a coin 50 times and get heads 25 times. What is the experimental probability of getting heads?
3. A jar has 20 candies (5 red, 15 green). If you pick a candy 10 times and get 3 red, what is the experimental probability of picking a red candy?
4. You conduct an experiment where you flip a coin and record the outcome 100 times. If you get heads 55 times, what is the experimental probability of heads?
5. A class has a survey on favourite fruits. Out of 30 students, 12 choose apples. What is the experimental probability of selecting a student who likes apples?
6. You roll two dice 30 times and get a total of 7 six times. What is the experimental probability of rolling a total of 7?
7. In a game, you draw a card from a 52-card deck 40 times, and you get a King 5 times. What is the experimental probability of drawing a King?
8. You conduct an experiment where you spin a spinner 80 times and it lands on yellow 20 times. What is the experimental probability of landing on yellow?
9. A survey shows that out of 50 people, 20 prefer coffee over tea. What is the experimental probability of choosing someone who prefers coffee?
10. If you conduct an experiment of rolling a die 100 times and get a 4 twenty-five times, what is the experimental probability of rolling a 4?

Hard Level Questions

1. If you roll a die 150 times and get a 6 twenty-five times, what is the experimental probability of rolling a 6?
2. A spinner has 5 equal sections. If you spin it 90 times and land on one section 45 times, what is the experimental probability of landing on that section?
3. You flip a coin 200 times and get heads 110 times. What is the experimental probability of tails?
4. You draw a card from a 52-card deck and replace it 100 times, drawing a Queen 10 times. What is the experimental probability of drawing a Queen?
5. You test a new product 75 times and it works 60 times. What is the experimental probability of it working?
6. A student tosses a coin 120 times and gets tails 50 times. What is the experimental probability of getting heads?
7. In a survey of 100 people, 40 prefer chocolate over vanilla. What is the experimental probability of selecting someone who prefers vanilla?
8. You roll a die 200 times and get a 3 forty times. What is the experimental probability of rolling a 3?
9. A class surveys 80 students about their favourite sport. If 32 prefer football, what is the experimental probability of choosing someone who prefers football?
10. You conduct an experiment of spinning a spinner with 8 sections 160 times and it lands on one section 40 times. What is the experimental probability of landing on that section?

Answers and Explanations

Easy Level Answers

1. $$\frac{6}{10} = 0.6$$
2. $$\frac{3}{12} = 0.25$$
3. $$\frac{2}{20} = 0.1$$
4. $$\frac{5}{15} = 0.33$$
5. $$\frac{3}{5} = 0.6$$
6. $$\frac{2}{5} = 0.4$$
7. $$\frac{8}{20} = 0.4$$
8. $$\frac{4}{24} = \frac{1}{6} \approx 0.17$$
9. $$\frac{10}{30} = \frac{1}{3} \approx 0.33$$
10. $$\frac{12}{40} = 0.3$$

Medium Level Answers

1. $$\frac{11}{60} \approx 0.183$$
2. $$\frac{25}{50} = 0.5$$
3. $$\frac{3}{10} = 0.3$$
4. $$\frac{55}{100} = 0.55$$
5. $$\frac{12}{30} = 0.4$$
6. $$\frac{6}{30} = 0.2$$
7. $$\frac{5}{40} = 0.125$$
8. $$\frac{20}{80} = 0.25$$
9. $$\frac{20}{50} = 0.4$$
10. $$\frac{25}{100} = 0.25$$

Hard Level Answers

1. $$\frac{25}{150} = \frac{1}{6} \approx 0.167$$
2. $$\frac{45}{90} = 0.5$$
3. $$\frac{90}{200} = 0.45$$
4. $$\frac{10}{100} = 0.1$$
5. $$\frac{60}{75} = 0.8$$
6. $$\frac{70}{120} = \frac{7}{12} \approx 0.583$$
7. $$\frac{60}{100} = 0.6$$
8. $$\frac{40}{200} = 0.2$$
9. $$\frac{32}{80} = 0.4$$
10. $$\frac{40}{160} = 0.25$$

By understanding experimental probability, you can make better predictions and understand the world around you! Keep practicing with different scenarios to improve your skills.