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Ch 3.3 Addition and Multiplication Rule

  • Page ID
    15894
  • Addition Rule:

    Addition Rule are used to find “OR” in a procedure.

    P(A or B) = P(A) + P(B) – P(A and B)

    If A and B are mutually exclusive: P(A and B) = 0

    P(A or B) = P(A)+ P (B) when A, B are mutually exclusive.

     

    Ex1.  Toss a 6-face die once, use addition rule method to find  P(one or odd).

    P(one or odd) = P(one) + P(odd) – P(one and odd)

                               = 1/6 + 3/6 – 1/6 = 3/6  =0.5

     

    Ex2.  Toss a 6-face die once, use addition rule method to find P( one or even) 

    Because one and even or mutully exclusive, so P (one or even) = P(one) + P(even)  =  1/6 + 3/6 = 0.667  

     

    Ex3. Use the contingency table below:

    contingency table

    GT = 51

    Use addition rule to find P(male or iPhone).

    P(male or iPhone) = P(male) + P(iPhone) – P(male and iPhone)   = 21/51 + 42/51 – 18/51 = (21+41-18)/51 =45/51 = 0.8823

     

    Multiplication Rule:

    Multiplication Rule is used to find probability of two events: A and B.

     \( \text{P(A and B)} = P(A) * P(B|A) \)

    If A and B are independent, P(B|A) = P(B) so

      \( \text{P(A and B)} = P(A) * P(B) \) when A, B are independent.

    A result of the multiplication rule gives the formula for conditional probability as:

    \(\\text{P(A given B)}=\text{P(A | B)} =\frac{\text{A and B}}{P(B)} \)

    Ex1: Given the two-way table below:

    contingency table

    Find P( male |iPhone) =  P( male and iPhone)/P(iPhone) =  \(\frac{18/51}{42/51} = \frac{18}{42} = 0.4286 \)

     

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