Addition rule for "OR"

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Introduction

Lessons

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Examples

Lessons

  1. Mutually Exclusive VS. Not Mutually Exclusive
    Consider the experiment of rolling a die.
    1. 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)
    2. 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)
    3. 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
    1. using the formula.
    2. using the Venn Diagram.
  3. A card is drawn from a standard deck of 52 cards. Determine the probability that:
    1. a heart or a spade is drawn.
    2. a heart or a face card is drawn.
    3. an ace or a face card is drawn.
    4. an ace or a spade is drawn.
  4. Use the following information to determine whether the events A, B are mutually exclusive.
    1. P(A)=0.5 P(A)=0.5
      P(B)=0.3P(B)=0.3
      P(A  P(A\;or  B)=0.7\;B)=0.7
    2. P(A)=23 P(A)=\frac{2}{3}
      P(B)=15P(B)=\frac{1}{5}
      P(A  P(A\;or  B)=1315\;B)=\frac{13}{15}
    3. P(A)=712 P(A)=\frac{7}{12}
      P(B)=513P(B)=\frac{5}{13}
      P(A  P(A\;and  B)=0\;B)=0

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Topic Basics
\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)