Mutually Exclusive Events – GCSE Maths

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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,

Probability formula for mutually exclusive events showing P(A intersection B) equals zero.

This means there is no overlap between the two events.

  • Mathematically,

Probability addition formula for mutually exclusive events showing P(A union B) equals P(A) plus P(B).

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

certified Physics and Maths tutorSolved 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:

Probability of rolling a 2 or 5 on a dice mutually exclusive events example.

Put the Values in formula,

Mutually exclusive events probability addition example GCSE maths.

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

Final Answer: 1/3

certified Physics and Maths tutorSolved 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:

Mutually exclusive events formula with P(A union B) equals P(A) plus P(B).

Step#3: Calculate the Probability:

Total marbles: 10 marbles

Mutually exclusive events probability example with fractions GCSE maths.

Put the Values in formula,

Mutually exclusive events probability calculation GCSE maths.

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

Final Answer: 1/2

certified Physics and Maths tutorSolved 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?

Mutually exclusive events playing cards hearts and clubs GCSE maths.

Solution: 

Step#1: Identify Events:

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

Step#2: Use Formula:

Mutually exclusive events formula with P(A union B) equals P(A) plus P(B).

Step#3: Calculate the Probability:

Total cards: 52 cards

Probabilities of mutually exclusive events playing cards GCSE maths.

Put the Values in formula,

Probability addition mutually exclusive events GCSE maths example.

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

Final Answer: 1/2

certified Physics and Maths tutorSolved 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:

Mutually exclusive events formula with P(A union B) equals P(A) plus P(B).

Step#3: Calculate the Probability:

Total Students: 30

Probability values of mutually exclusive events GCSE maths.

Put the Values in formula,

Example showing addition of probabilities for mutually exclusive events in GCSE maths.

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

Final Answer: 2/3

certified Physics and Maths tutorSolved 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:

Mutually exclusive events formula with P(A union B) equals P(A) plus P(B).

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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