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28 July, 02:20

What is the difference between the product rule for independent and dependent events?

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  1. 28 July, 03:45
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    Independent Events The probability of one event happening isn't influenced by the outcome of another.

    In mathematical terms

    A

    ,

    B

    events

    ,

    P

    (

    A



    B

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    =

    P

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    )



    P

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    B

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    This reads: Probability of A and B happening is equal to the probability of A happening multiplied by the probability of B happening

    An equivalent definition

    P

    (

    A



    B

    )

    =

    P

    (

    A

    )

    This reads: The probability of A given B happened is equal the probability of A

    Example:

    Event A: Rolling a number larger than four on a die in the first roll Event B: Rolling a 6 on a die on the second roll. These events are independent because one roll of a dice doesn't influence the outcome of another dice roll.

    Dependent Events Is the oposite. If the outcome of one event influences the probability of the other they aren't independent

    P

    (

    A



    B

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    P

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    A

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    Example:

    Event A: Rolling a number larger than four on a die Event B: Rolling a 6 on a die on the same roll. These events are dependent because, as we are in the same dice roll, the occurrence of event B changes the probability of event A, actually it makes it 1.
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