Year 7 Maths: Probability of Simple Events and Opposite Events

Introduction to Probability

Today, we will explore the exciting world of probability. Probability helps us understand how likely an event is to happen.

What is Probability?

Probability is a way of expressing the chance of an event occurring. We often use a scale from 0 to 1 or as a percentage from 0% to 100%.

• 0% means the event will not happen (impossible).
• 100% means the event will definitely happen (certain).
• Anything in between represents different levels of likelihood.

Simple Events

A simple event is one specific outcome from a situation. For example, if you roll a die, the possible simple events are getting a 1, 2, 3, 4, 5, or 6.

Example of Simple Events

If you flip a coin, the simple events are:

• Getting Heads
• Getting Tails

Calculating Probability of Simple Events

To find the probability of a simple event, we can use this formula:

$$\text{Probability} = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$$

Example Calculation

If you roll a fair six-sided die, the probability of rolling a 3 is:

$$\text{Probability of rolling a 3} = \frac{1}{6}$$

There is 1 favourable outcome (rolling a 3) and 6 possible outcomes (1, 2, 3, 4, 5, or 6).

Opposite Events

An opposite event is what does NOT happen. If one event occurs, its opposite event is the one that cannot occur at the same time.

Example of Opposite Events

Using the coin flip example:

• The event of getting Heads has the opposite event of getting Tails.

Understanding Opposite Events

The probability of an event and its opposite add up to 1 (or 100%).

$$\text{Probability of event} + \text{Probability of opposite event} = 1$$

Example Calculation

If the probability of rolling a 3 is $$\frac{1}{6}$$ , then the probability of NOT rolling a 3 is:

$$\text{Probability of NOT rolling a 3} = 1 – \frac{1}{6} = \frac{5}{6}$$

So, you have a 5 out of 6 chance of rolling something other than a 3.

Key Rules to Remember

1. Total Probability = 1: The probabilities of all possible outcomes must equal 1.
2. Opposite Events: The probability of an event and its opposite add up to 1.
3. Favourable Outcomes: Count only the outcomes you are interested in when calculating probability.

Tips and Tricks

• Always list all possible outcomes before calculating probability.
• Remember that probabilities can also be expressed as percentages—just multiply by 100!
• Practice makes perfect! Solve various problems to strengthen your understanding.

Questions

Easy Level Questions (20)

1. What is the probability of rolling a 1 on a six-sided die?
2. If you flip a coin, what is the probability of getting Heads?
3. What is the probability of getting a number greater than 4 on a die?
4. If you pick a card from a standard deck, what is the probability of drawing a heart?
5. What is the probability of rolling an even number on a die?
6. If you flip a coin, what is the probability of getting Tails?
7. What is the probability of rolling a number less than 5 on a die?
8. What is the probability of getting a 6 when rolling a die?
9. If you pull a marble from a bag containing 3 red, 2 blue and 5 green marbles, what is the probability of getting a red marble?
10. What is the probability of rolling a number that is not a 1 on a die?
11. What is the probability of getting a 2 or a 3 when rolling a die?
12. If you flip two coins, what is the probability of getting at least one Heads?
13. What is the probability of drawing an Ace from a deck of cards?
14. What is the probability of not drawing a King from a deck of cards?
15. If you roll a die, what is the probability of rolling a number that is a multiple of 3?
16. What is the probability of picking a blue marble from a bag with 10 marbles that are all red?
17. If you flip a coin twice, what is the probability of getting at least one Heads?
18. What is the probability of rolling a 5 or a 6 on a die?
19. If you draw a card from a standard deck, what is the probability of drawing a Spade?
20. What is the probability of rolling a die and getting a number less than 3?

Medium Level Questions (20)

1. What is the probability of selecting a yellow marble if there are 4 yellow, 3 red, and 5 green marbles?
2. If you roll two dice, what is the probability of getting a total of 7?
3. If a bag has 3 white, 2 black, and 1 red ball, what is the probability of picking a black ball?
4. What is the probability of rolling at least one 4 when rolling two dice?
5. If you flip three coins, what is the probability of getting exactly two Heads?
6. What is the probability of drawing a queen from a standard deck of cards?
7. If you roll a die twice, what is the probability of getting the same number both times?
8. What is the probability of drawing a red card or a face card from a deck of cards?
9. If you roll a die, what is the probability of rolling a number greater than 2 and less than 5?
10. If a spinner is divided into 5 equal sections (1, 2, 3, 4, 5), what is the probability of landing on an odd number?
11. What is the probability of not rolling a 6 with two dice?
12. If a student has a 75% chance of passing a test, what is the probability of not passing the test?
13. In a class of 30 students, 18 are girls. What is the probability of randomly selecting a boy?
14. If you flip a coin five times, what is the probability of getting at least one Tails?
15. What is the probability of drawing a numbered card from a standard deck of cards?
16. If there are 10 marbles in a bag (4 blue, 3 green, 3 red), what is the probability of not drawing a blue marble?
17. What is the probability of rolling a 2 or a 5 on a die?
18. If a box contains 5 apples and 3 bananas, what is the probability of selecting a banana?
19. If you draw two cards from a deck without replacement, what is the probability both are Spades?
20. What is the probability of rolling a number less than 4 on two dice?

Hard Level Questions (20)

1. If a box contains 4 yellow, 6 blue, and 10 green marbles, what is the probability of picking a green marble?
2. What is the probability of rolling a sum of 9 when rolling two dice?
3. If you draw two cards from a standard 52-card deck without replacement, what is the probability that both are Aces?
4. If a die is rolled three times, what is the probability of getting at least one 1?
5. What is the probability of selecting a prime number when rolling a die?
6. If a spinner has 8 equal sections (1-8), what is the probability of landing on a number greater than 5?
7. What is the probability of rolling at least one 3 when rolling three dice?
8. If you flip a coin 6 times, what is the probability of getting exactly 4 Heads?
9. If a bag contains 3 red, 4 blue, and 5 green marbles, what is the probability of selecting two marbles of different colours?
10. What is the probability of drawing a heart or a diamond from a deck of cards?
11. If you roll two dice, what is the probability of getting a double?
12. If you select two students from a class of 20 (10 boys and 10 girls), what is the probability both are girls?
13. What is the probability of rolling a number between 3 and 5 (inclusive) on a die?
14. If a box contains 2 red, 3 blue, and 5 green balls, what is the probability of drawing a blue ball on the first draw and a red ball on the second?
15. If you flip a coin 10 times, what is the probability of getting exactly 6 Heads?
16. If you have a set of 10 cards numbered 1 to 10, what is the probability of drawing a card that is a multiple of 4?
17. What is the probability of rolling a score of 2 or 12 with two dice?
18. If you have a bag with 2 green, 2 red, and 4 blue marbles, what is the probability of picking a blue marble first and a green marble second?
19. If you roll a die and flip a coin, what is the probability of rolling an even number and getting Tails?
20. In a lottery where you choose 5 numbers from 1 to 50, what is the probability that your numbers match exactly 3 winning numbers?

Answers and Explanations

Easy Level Answers

1. $$\frac{1}{6}$$
2. $$\frac{1}{2}$$
3. $$\frac{2}{6} = \frac{1}{3}$$
4. $$\frac{13}{52} = \frac{1}{4}$$
5. $$\frac{3}{6} = \frac{1}{2}$$
6. $$\frac{1}{2}$$
7. $$\frac{4}{6} = \frac{2}{3}$$
8. $$\frac{1}{6}$$
9. $$\frac{3}{10}$$
10. $$\frac{5}{6}$$
11. $$\frac{2}{6} = \frac{1}{3}$$
12. $$\frac{7}{8}$$
13. $$\frac{4}{52} = \frac{1}{13}$$
14. $$\frac{48}{52} = \frac{12}{13}$$
15. $$\frac{2}{6} = \frac{1}{3}$$
16. $$0$$
17. $$\frac{1}{8}$$
18. $$\frac{1}{5}$$
19. $$\frac{1}{4}$$
20. $$\frac{1}{6}$$

Medium Level Answers

1. $$\frac{4}{9}$$
2. $$\frac{6}{36} = \frac{1}{6}$$
3. $$\frac{1}{6}$$
4. $$\frac{21}{36} = \frac{7}{12}$$
5. $$\frac{3}{8}$$
6. $$\frac{4}{52} = \frac{1}{13}$$
7. $$\frac{6}{36} = \frac{1}{6}$$
8. $$\frac{28}{52} = \frac{7}{13}$$
9. $$\frac{2}{6} = \frac{1}{3}$$
10. $$\frac{3}{10}$$
11. $$\frac{25}{36}$$
12. $$\frac{1}{4}$$
13. $$\frac{2}{10} = \frac{1}{5}$$
14. $$\frac{1}{16}$$
15. $$\frac{1}{13}$$
16. $$\frac{7}{10}$$
17. $$\frac{1}{3}$$
18. $$\frac{4}{10} = \frac{2}{5}$$
19. $$\frac{1}{221}$$
20. $$\frac{5}{36}$$

Hard Level Answers

1. $$\frac{10}{20} = \frac{1}{2}$$
2. $$\frac{4}{36} = \frac{1}{9}$$
3. $$\frac{4}{52} \cdot \frac{3}{51} = \frac{12}{2652} = \frac{1}{221}$$
4. $$\frac{1}{6}$$
5. $$\frac{3}{6} = \frac{1}{2}$$
6. $$\frac{3}{8}$$
7. $$\frac{1}{2}$$
8. $$\frac{5}{32}$$
9. $$\frac{64}{90} = \frac{32}{45}$$
10. $$\frac{26}{52} = \frac{1}{2}$$
11. $$\frac{6}{36} = \frac{1}{6}$$
12. $$\frac{10}{20} = \frac{1}{2}$$
13. $$\frac{2}{6} = \frac{1}{3}$$
14. $$\frac{8}{20} = \frac{2}{5}$$
15. $$\frac{252}{1024} = \frac{63}{256}$$
16. $$\frac{2}{10} = \frac{1}{5}$$
17. $$\frac{1}{36}$$
18. $$\frac{5}{36}$$
19. $$\frac{2}{20} = \frac{1}{10}$$
20. $$\frac{1}{2,118,760}$$

I hope this lesson on the probability of simple events and opposite events was helpful! Remember to review the concepts and practice the questions to strengthen your understanding. Happy studying!