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IBMathsDPApplications & Interpretation (AI)HLRevision Notes4. Statistics & ProbabilityProbabilityIndependent & Mutually Exclusive Events

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

Roger B

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Roger B

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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

  • 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 formula booklet

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

      • This occurs because 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 these two events

    • 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

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    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.