Addition rule for "OR"
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- Mutually Exclusive VS. Not Mutually Exclusive
Consider the experiment of rolling a die.- Event A: an even number is thrown
Event B: an odd number is thrown
i) List the outcomes for:
⋅ event A
⋅ event B
⋅ event A or B
⋅ event A and B
ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
iii) Determine the following probabilities:
⋅ P(A)
⋅ P(B)
⋅ P(A or B)
⋅ P(A and B)
- Event A: an even number is thrown
Event B: a multiple of three is thrown
i) List the outcomes for:
⋅ event A
⋅ event B
⋅ event A or B
⋅ event A and B
ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
iii) Determine the following probabilities:
⋅ P(A)
⋅ P(B)
⋅ P(A or B)
⋅ P(A and B)
- Supplementary info on mutually exclusive and addition rule.
- Event A: an even number is thrown
- 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 card is drawn from a standard deck of 52 cards. Determine the probability that:
- Use the following information to determine whether the events A, B are mutually exclusive.
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Topic Notes
⋅ P(A or B): probability of event A occurring or event B occurring during a single trial.
⋅ 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)
⋅ 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)
⋅ 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)
⋅ 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)
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