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Probability Recap

Probability Recap. Vocabulary. Probability The likelihood of an event Theoretical is what should happen. Experimental is what does happen. Sample Space The set of all possible outcomes Event A subset of the sample space. Vocabulary. Complement of an Event

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Probability Recap

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  1. Probability Recap

  2. Vocabulary • Probability • The likelihood of an event • Theoretical is what should happen. • Experimental is what does happen. • Sample Space • The set of all possible outcomes • Event • A subset of the sample space

  3. Vocabulary • Complement of an Event • When an event does NOT occur • If A is the event that it rains, A’ is the event that it does not rain • Can be noted A’, Ac, A, or ~A

  4. The Complement of a Set The complement of a set A is defined as the set of elements that are contained in U, the universal set, but not contained in set A. The symbolism and notation for the complement of set A are In the Venn diagram on the left, the rectangle represents the universe. A is the shaded area outside the set A.

  5. Union of Sets The union of two sets A and B is the set of all elements formed by combining all the elements of set A and all the elements of set B into one set. It is written AB. A OR B In the Venn diagram on the left, the union of A and B is the entire region shaded. B A

  6. Intersection of Sets The intersection of two sets A and B is the set of all elements that are common to both A and B. It is written A  B. A AND B In the Venn diagram on the left, the intersection of A and B is the shaded region. B A

  7. Disjoint Sets If two sets have no elements in common, they are said to be disjoint.Two sets A and B are disjoint if A  B = . Example: The rational and irrational numbers are disjoint.

  8. Vocabulary • Independent Events • Events are independent if the probability of one does not affect the probability of the other • Dependent Events • Events are dependent if the probability of one DOES affect the probability of the other • Mutually Exclusive (a.k.a. Disjoint) • Events are mutually exclusive if they cannot occur at the same time

  9. What’s the Difference Between Independent and Mutually Exclusive? Mutually Exclusive:Two Events, One Trial. Rolling a 2 and rolling a 4 on one roll of a die. Independent: Two events, Two Trials. Rolling a 2 and then rolling a 4. Sometimes you need to use the conditional probability formula to tell whether events are independent or not.

  10. Conditional Probability • Always for two events or trials P(A and B) = P(A) * P(B|A) If the trials are independent, then P(B|A) = P(B)

  11. Relate: P( male ) = 58% P( male and jogs ) = 20% P( A and B ) P( A ) Write: P(B|A) = 0.2 0.58 = Substitute 0.2 for P(A and B) and 0.58 for P(A). 0.344 Simplify. Conditional Probability Researchers asked people who exercise regularly whether they jog or walk. Fifty-eight percent of the respondents were male. Twenty percent of all respondents were males who said they jog. Find the probability that a male respondent jogs. Define: Let A = male. Let B = jogs. The probability that a male respondent jogs is about 34%.

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