Revision NotesExam QuestionsFlashcardsPast PapersMock Exams
IBMathsDPApplications & Interpretation (AI)HLRevision Notes4. Statistics & ProbabilityProbabilityIndependent & Mutually Exclusive Events

Independent & Mutually Exclusive Events (DP IB Applications & Interpretation (AI)): Revision Note

Roger B

Written by: Roger B

Reviewed by: Dan Finlay

Updated on

DP Applications & Interpretation (AI): HLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SLDP Applications & Interpretation (AI): SLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SL

Independent & mutually exclusive events

What are mutually exclusive events?

  • Two events are mutually exclusive if they cannot both occur

    • For example: when rolling a dice the events "getting a prime number" and "getting a 6" are mutually exclusive

  • If A and B are mutually exclusive events then:

    • straight P left parenthesis A intersection B right parenthesis equals 0

What are independent events?

  • Two events are independent if one occurring does not affect the probability of the other occurring

    • For example: when flipping a coin twice the events “getting a tails on the first flip” and “getting a tails on the second flip” are independent

  • If A and B are independent events then

    • straight P left parenthesis A vertical line B right parenthesis equals straight P left parenthesis A right parenthesis and straight P left parenthesis B vertical line A right parenthesis equals straight P left parenthesis B right parenthesis

      • That is just the maths way of saying 'one occurring does not affect the probability of the other occurring'!

  • If A and B are independent events then

    • straight P left parenthesis A intersection B right parenthesis equals straight P left parenthesis A right parenthesis straight P left parenthesis B right parenthesis 

      • This is given in the exam formula booklet

      • This is a useful formula to test whether two events are independent

How do I find the probability of combined mutually exclusive events?

  • If A and B are mutually exclusive events then

    • straight P open parentheses A union B close parentheses equals straight P open parentheses A close parentheses plus straight P open parentheses B close parentheses

      • This is given in the exam formula booklet

      • This occurs because for mutually exclusive events straight P open parentheses A intersection B close parentheses equals 0

  • For any two events A and B:

    • The events A intersection B and A intersection B apostrophe are mutually exclusive

    • and A is the union of those two events

      • i.e. A equals open parentheses A intersection B close parentheses union open parentheses A intersection B apostrophe close parentheses

    • Therefore

      • straight P left parenthesis A right parenthesis equals straight P left parenthesis A intersection B right parenthesis plus straight P left parenthesis A intersection B apostrophe right parenthesis

    • This works for any two events A and B

Worked Example

a) A student is chosen at random from a class. The probability that they have a dog is 0.8, the probability they have a cat is 0.6 and the probability that they have a cat or a dog is 0.9.
Find the probability that the student has both a dog and a cat.

4-3-1-ib-ai-aa-sl-types-of-events-a-we-solution

b) Two events, Q and R, are such that straight P left parenthesis Q right parenthesis equals 0.8 and straight P left parenthesis Q intersection R right parenthesis equals 0.1.
Given that Q and R are independent, find straight P left parenthesis R right parenthesis.

4-3-1-ib-ai-aa-sl-types-of-events-b-we-solution

c) Two events, S and T, are such that straight P left parenthesis S right parenthesis equals 2 straight P left parenthesis T right parenthesis.
Given that S and T are mutually exclusive and that straight P left parenthesis S union T right parenthesis equals 0.6 find straight P left parenthesis S right parenthesis and straight P left parenthesis T right parenthesis.

4-3-1-ib-ai-aa-sl-types-of-events-c-we-solution

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourself
    Previous:Probability & Types of EventsNext:Conditional Probability
    Author
    Reviewer
    Roger B

    Author: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.