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6.3 Conditional Probabilities

6.3 Conditional Probabilities. Age and Marital Status of women (in thousands). What is the probability of a woman being married? P(married) = 58,929 = .592 99,585. What is the probability of a woman being aged 18 to 24 and married?

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6.3 Conditional Probabilities

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  1. 6.3 Conditional Probabilities

  2. Age and Marital Status of women (in thousands) What is the probability of a woman being married? P(married) = 58,929 = .592 99,585

  3. What is the probability of a woman being aged 18 to 24 and married? P(18 to 24 & married) = 3,046 = .031 99,585

  4. Conditional Probability • Often probabilities will change if we have some other information. • Do you expect the probability of a woman being married given that she is aged 18 to 24 to be the same as the general population? P(married) was .592.

  5. What is the probability of a woman being married given that she is 18 to 24? P(married | 18 to 24) = 3,046/12,614 = .241

  6. P(married) = .592 = P(married | 18 to 24) = .241 = P(married & 18 to 24) = .031 = • The relationship between all three P(married & 18 to 24) = P(married)·P(married|18 to 24) .031 = .592 · .241

  7. General Multiplication Rule • P(A and B) = P(A)·P(B|A) In words this means that for both events to occur, first one one must occur, then, given that the first event has occurred, the second must occur.

  8. Definition of Conditional Probability

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