Download 5.3 Conditional Probability, Dependent Events, Multiplication Rule

Statistics Notes: 5.3 Conditional Probability, Dependent Events, Multiplication Rule
5.3 Conditional Probability and the Multiplication Rule
Two members from a 5­member committee are to be randomly selected to serve as chairperson and secretary. The 1st person selected will be the chair and the 2nd will be the secretary. The members of the committee are Bob, Faye, Elena, Melody and Dave. What is the probability that Elena is the chair and Dave is secretary?
Secretary
Chair
Multiplication Rule: For any two events E and F, P(E and F) = P(E) P(F|E)
Conditional Probability: For any 2 events E and F, P(F|E)
read as "the probability of F given E"
The probability that F happens given that E happened
The probability that a police officer is using his radar to check speeds on highway 47 is 0.08. The probability that a randomly selected driver is speeding, given that the police officer is checking speeds is 0.2. What is the probability that a driver is speeding and there is a police officer checking speeds?
Dependent Events: The probability of 1 event is changed by a 2nd event.
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Statistics Notes: 5.3 Conditional Probability, Dependent Events, Multiplication Rule
In roulette, there is a wheel with slots numbered 0, 00, and 1 through 36. A metal ball is allowed to roll around a wheel until it falls into one of the numbered slots. You decide to play the game and place a bet on the number 17. What is the probability the ball will land in the slot numbered 17 twice in a row?
Independent Events: The probability of 1 event is not changed by a 2nd event.
2 events, E and F, are independent if and only if
P(E|F) = P(E) and P(F|E) = P(F)
A card is randomly drawn from a standard deck of cards. Are the events "draw an Ace" and "draw a Club" independent events?
P(Ace)
P(Ace|Club)
P(Club)
P(Club|Ace)
Is this the same as asking if they are mutually exclusive? NO!
P(Ace|Club)
P(Club|Ace)
According to a national vital statistics report, the probability that a randomly selected 24 year old male will survive the year is 99.85%. What is the probability that 3 randomly selected 24 year old males will survive the year?
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Statistics Notes: 5.3 Conditional Probability, Dependent Events, Multiplication Rule
In a survey of 10,000 African­Americans, it was determined that 27 had sickle cell anemia (SCA).
If 1 person is randomly selected, find P(he/she has SCA).
If two people are randomly selected, find P(both have SCA).
If two people are randomly selected, find P(both have SCA) assuming independence.
If small random samples are taken from large populations without replacement, it is reasonable to assume independence of the events. As a general rule, if the sample size is less than 5% of the population, then treat the events as independent.
Find the probability that at least 1 male out of 1000, aged 24, will die during the course of the year if the probability that a randomly selected 24 year old male survives the year is 99.85%.
HW: p293 C&V #1 ­ 3, 5 ­ 6; p293 #1 ­ 27odd
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