Addition rule for "OR"

Addition rule for "OR"

Lessons

\cdot P(A or B): probability of event A occurring or event B occurring during a single trial.

\cdot If events A, B are mutually exclusive:
- events A, B have no common outcomes.
- in the Venn Diagram, the circle for A and the circle for B have no area of overlap.
- P(A or B) = P(A) + P(B)

\cdot If events A, B are not mutually exclusive:
- events A, B have common outcomes.
- in the Venn Diagram, the circle for A and the circle for B have an area of overlap representing the event "A and B".
- P(A or B) = P(A) + P(B) – P(A and B)
  • Introduction

  • 1.
    Mutually Exclusive VS. Not Mutually Exclusive
    Consider the experiment of rolling a die.
    a)
    Event A: an even number is thrown
    Event B: an odd number is thrown
    i) List the outcomes for:
    \cdot event A
    \cdot event B
    \cdot event A or B
    \cdot event A and B
    ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
    iii) Determine the following probabilities:
    \cdot P(A)
    \cdot P(B)
    \cdot P(A or B)
    \cdot P(A and B)

    b)
    Event A: an even number is thrown
    Event B: a multiple of three is thrown
    i) List the outcomes for:
    \cdot event A
    \cdot event B
    \cdot event A or B
    \cdot event A and B
    ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
    iii) Determine the following probabilities:
    \cdot P(A)
    \cdot P(B)
    \cdot P(A or B)
    \cdot P(A and B)

    c)
    Supplementary info on mutually exclusive and addition rule.


  • 2.
    There are 20 students in a class. 9 students like pizza and 7 students like pasta. Of these students, 3 students like both. Determine the probability that a randomly selected student in the class like pizza or pasta
    a)
    using the formula.

    b)
    using the Venn Diagram.


  • 3.
    A card is drawn from a standard deck of 52 cards. Determine the probability that:
    a)
    a heart or a spade is drawn.

    b)
    a heart or a face card is drawn.

    c)
    an ace or a face card is drawn.

    d)
    an ace or a spade is drawn.


  • 4.
    Use the following information to determine whether the events A, B are mutually exclusive.
    a)
    P(A)=0.5 P(A)=0.5
    P(B)=0.3P(B)=0.3
    P(AP(A\;orB)=0.7\;B)=0.7

    b)
    P(A)=23 P(A)=\frac{2}{3}
    P(B)=15P(B)=\frac{1}{5}
    P(AP(A\;orB)=1315\;B)=\frac{13}{15}

    c)
    P(A)=712 P(A)=\frac{7}{12}
    P(B)=513P(B)=\frac{5}{13}
    P(AP(A\;andB)=0\;B)=0


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