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# Applied Math 40S Slides Mar 2, 2007

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Independent and dependent probability. Also testing for independence.

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### Applied Math 40S Slides Mar 2, 2007

1. 1. Phone Numbers A computer is used to generate random telephone numbers. Of the numbers generated and in service, 56 are unlisted and 144 are listed in the telephone directory. If one of these telephone numbers is randomly selected, what is the probability that it is unlisted? 9.5’! '3' 294 or: P/ Kan/ E / wmzzzx 9‘, /9, : ‘/95-3 S 4+/9/4;: zoo wt /72
2. 2. Marbles A jar contains 5 red and 7 blue marbles. What is the probability of pulling out 2 blue marbles in a row, with replacement? /1 /3~. /. { 7 -: 97 57:6? /77 Tr \$3 : _0.37/
3. 3. Marbles (again) Ajar contains 5 red and 7 blue marbles. What is the probability of pulling out 2 blue marbles in a row, without replacement? -"X, — ll Viz ll /12' '»r’.7‘= w~, ‘i‘ 1 l5‘». ’F
4. 4. Dependent and independent probabilities You toss a coin and roll a die 6. What is the probability that you get (heads, 6)‘?
5. 5. 1ndependent_E1ents Events in which the outcome of one event does not affect the outcome of the other event. DICTIONARY Dependent an - independent pmbabilities A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and then replaced back in the bag. A second marble is selected, what is the probability that it is blue?
6. 6. Dependent Events If the outcome of one event affects the outcome of another event, then the events are said to be dependent events. DICTIONARY Dependent and independent probabilities A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and NOT replaced back in the bag. A second marble is selected, wp; i't(is the, 0 L13» _ probability that it is blue? 7) > ‘ _U - (RR :
7. 7. Examples: Which of the following are dependent events‘? Which are independent? 1. g (s£c€g7r, andomly) three red marbles without replacement from a bag that contains six red and nine blue marbles. 2. Seledtlilrigb red card from a deck of cards, returning the card to the deck, shuffling the cards, and selecting a second red card. 141.? ) 3. Rolling two dice. 4. The weather and how likely you are to go visiting. You have decided that there is a 50% chance that you will visit your friend if it does not snow, and a 10% chance ifit does snow. )5»
8. 8. Testing for independence 30% of seniors get the ﬂu every year. 50% of seniors get a flu shot annually. 10% of seniors who get the ﬂu shot also get the flu. Are getting a flu shot and getting the ﬂu independent events? f/ Jug/ Cot? - 0'/ S ? (9**“7<tF“')= do/0
9. 9. Testing for independence 30% of seniors get the ﬂu every year. 50% of seniors get a ﬂu shot annually 19% of seniors who get the re getting a ﬂu shot and getting’ u in ependent events? '
10. 10. The probability that Gallant Fox will win the first race is 2/ 5 and that Nashau will win the second race is 1/3. I. ‘ 7__ _ 1. What'i's'ifii"é" probability that both horses will win their respective races? _, P(é <1) ; " I ___" . 1 _ ‘L S7 2. / § 2. What is the probability that both horses will lose their respective races? ‘, , /2 '5 3. What is the probability that at least one horse will win a race? I ‘s S}; s: re