Mutually Exclusive Events – GCSE Maths

Introduction

Studying Mutually exclusive events are essential in probability because they help us analyze different types of real-world situations where outcomes interact in different ways.
We learn mutually exclusive events in probability to understand situations where two events cannot happen at the same time.

What are Mutually Exclusive Events?

Mutually exclusive events are events that cannot happen at the same time.
For example: When you roll an ordinary dice, you cannot get a 3 and an even number at the same time.
Two events A and B are Mutually exclusive if,

This means there is no overlap between the two events.

Mathematically,

Steps To Solve The Mutually Exclusive Events

Here are the steps to solve problems in probability:

Steps To Solve:

Step#1: Identify Events
Step#2: Use Formula
Step#3: Calculate the Probability

Solved Example

Problem: A fair six-sided die is rolled. What is the probability of rolling a 2 or a 5?

Solution:

Step#1: Identify Events:

- Event A: Rolling a 2.
- Event B: Rolling a 5.

Step#2: Use Formula:

Step#3: Calculate the Probability:

Put the Values in formula,

The Probability of rolling a 2 or a 5 is 1/3

Final Answer: 1/3

Solved Example

Problem: A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. If one marble is drawn at random, what is the probability that it is red or blue?

Solution:

Step#1: Identify Events:

- Event A: Drawing a red marble
- Event B: Drawing a blue marble

Step#2: Use Formula:

Step#3: Calculate the Probability:

Total marbles: 10 marbles

$Mutually exclusive events probability example with fractions GCSE maths.$

Put the Values in formula,

The Probability of drawing a Red or Blue marble is 1/2

Final Answer: 1/2

Solved Example

Problem: A card is drawn from a standard deck of 52 cards. What is the probability that the card is either a Heart or a Club?

Solution:

Step#1: Identify Events:

- Event A: Drawing a Heart: 13 Hearts
- Event B: Drawing a Club: 13 Clubs

Step#2: Use Formula:

Step#3: Calculate the Probability:

Total cards: 52 cards

Put the Values in formula,

The probability of drawing either a Heart or a Club from a deck is 1/2

Final Answer: 1/2

Solved Example

Problem: In a class of 30 students, each child likes different subjects, such as

12 students like Math(M)
8 students like Science(S)
10 students like History(H)

If a student is selected at random, what is the probability that the student likes math or science?

Solution:

Step#1: Identify Events:

- Event A: Student like Math: 12
- Event B: Student like Science: 8

Step#2: Use Formula:

Step#3: Calculate the Probability:

Total Students: 30

Put the Values in formula,

The probability that a randomly chosen student likes either math or science is 2/3

Final Answer: 2/3

Solved Example

Problem: A pizza is cut into 8 equal slices:

3 slices have cheese topping(C)
2 slices have pepperoni topping(P)
3 slices have veggie topping(V)

If a person randomly picks one slice, what is the probability that it is cheese or pepperoni?

Solution:

Step#1: Identify Events:

- Event A: Cheese slices: 3
- Event B: Pepperoni: 2

Step#2: Use Formula:

Step#3: Calculate the Probability:

Total Slices: 8

$Mutually exclusive events probabilities with fractions for GCSE maths.$

Put the Values in formula,

$Mutually exclusive events probability calculation with fractions for GCSE maths.$

The probability of picking a cheese or pepperoni slice is 5/8

Final Answer: 5/8

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