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Warm-up

Warm-up. A statistical report states that 68% of adult males in China smoke. What is the probability that five randomly selected adult males from China are smokers?. Compound Events (Dependent) – Part II. Calculate a probability that is associated with compound events that are dependent.

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Warm-up

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  1. Warm-up • A statistical report states that 68% of adult males in China smoke. What is the probability that five randomly selected adult males from China are smokers?

  2. Compound Events (Dependent) – Part II Calculate a probability that is associated with compound events that are dependent

  3. Dependent • Events A and B are dependent if the occurrence of one event will affect the probability of the other event to occur.

  4. Example of two dependent events • If you complete all your homework, it will certainly affect the probability that you will understand the material.

  5. Conditional probability • Given any two events, A and B, P(A|B) means the probability that event A occurs, given that event B has already occurred.

  6. Formula For Dependent Events A and B OR Since Then,

  7. Math Flash!!! • If A and B are actually independent events, then P(B|A) really means the same as P(B). The reason is because, for two independent events, the occurrence of one of them has no effect on the probability that the other event will occur.

  8. Example of conditional probability • In drawing two cards from a deck of cards, one at a time, with no replacement, what is the probability of drawing an ace, followed by a jack? • Let A = drawing an ace for the first card • Let B = drawing a jack for the second card • Then P(A)= ; P(B|A)=

  9. Example of conditional probability • In drawing two cards from a deck of cards, one at a time, with no replacement, what is the probability of drawing a red picture card, followed by either a 9 or 10? • Let C = drawing a red picture card • Let D = drawing either a 9 or 10 card • Then P(C)= ; P(D|C)=

  10. Favorite type of music of 100 people Suppose 2 people are selected from this group, one at a time, with no replacement. What is the probability that the favorite type of music for the first person in Rhythm and Blues, and the favorite type of music for the second person is Oldies? Let G = Rhythm and Blues Let H = Oldies

  11. Favorite type of music of 100 people What is the probability of selecting 2 people, one at a time, for whom Jazz is their favorite type of music? Let J = Jazz Let K = Jazz

  12. Seeking the value of P(B|A)

  13. The probability that it will rain today is 0.24. The probability that it will rain today and tomorrow is 0.15. What is the probability that it will rain tomorrow, given that it rains today? • Let A = it rains today • Let B = it rains tomorrow

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