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.

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Presentation transcript:

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?

Calculate a probability that is associated with compound events that are dependent

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

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

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

Formula For Dependent Events A and B OR Since Then,

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.

Example of conditional probability Let A = drawing an ace for the first card Let B = drawing a jack for the second card 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? Then P(A)= ; P(B|A)=

Example of conditional probability Let C = drawing a red picture card Let D = drawing either a 9 or 10 card 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? Then P(C)= ; P(D|C)=

Favorite type of music of 100 people Type of MusicFrequency Country20 Rhythm and Blues 25 Oldies35 Jazz10 All Others10 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

Favorite type of music of 100 people Type of MusicFrequency Country20 Rhythm and Blues 25 Oldies35 Jazz10 All Others10 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

Seeking the value of P(B|A)

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