~ e.o-c- - Mr. Casas' Weeblymrcasas.weebly.com/uploads/5/2/2/5/5225628/6.3_practice_answers.pdf · Isabel Briggs Myers was a pioneer in the study of personality types. The personality

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6.3 - Probabili!y

1. Type of BirthSingle Birtl1Twins

TripletsQuadruplets

Number of Births41,500,OQO500,0005,000100

EventABCD

Use this information to approximate the probability that a randomly selected pregnantwoman who reaches full term

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b. P(D) -=- . DO0002-

c. P(AC)- .. orz. 0

2, A student placement center has requests from five students for interviews regardingemployment with a particular consulting firm. Three of these students are math majors, andthe other two are statistics majors, Unfortunately, the interviewer has time to talk to two ofthe students; these will be randomly selected from the five,

a. What is the probability that botb selected students are S~a '

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' cs majors?

, .. lis ( '/4) ::. 7,/ fL,O :. . Lb, What IS the probabIlIty that both students are math maJ -

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.:udents have different ~ors~ I. -~

. \ - ?L<ScqY'e~;: ,- (.1 +o~) -~3, In a survey, 200 students are asked whether or not they like to watch basketball or football on

television. Of the 200 students, 110 like to watch football, 80 like to watch basketball and 50like to watch both,

a, Draw a Venn Diagram to describe the results of the survey.

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b. What is the probabilitythat a studentlikedto watch football?~ ' ,/ 3)c. What is the probability that a student liked to watch only football? *L\V -:t~--j .(( Jd. What is the probability that a student liked to watch football or basketball? ~ ~e, What is the probability that a student did not like to watch either sport? "Z-1J'u

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4. A veterinarian tells you that if you breed two cream-colored guinea pigs, the probability thatan offspring will be pure white is 0.25. Wh.§tis the probability that it will not be pure white?

( ~.5)5. How do you find out about ajob? The national Center for Career Strategies, Inc., has data on

information sources that have led to actual jobs. Data adapted from a report in USA Todayshow sources for 1000jobs selected at random:

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a. Use these data to estimate the probability that ajob selected at random would havethe listed source.

b. How can we verify to see if our answers to part "a" are correct? ~ \16WJ cuJ.-t).-fb ~~ I >()..'"tt

. . . .. . . . e.o-c-r1 ", r .:II,,' 'c. What ISthe probabIlIty of someone obtaInIng a Job from a mass mal mg or 0 .!- P 4- 1

networking? Describe two ways of making this calculation. "

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d. What is the probability of someone obtaining a job that did not network? Describe

two ways Qf making thj .calculation 0&

6. Isabel Briggs Myers was a pioneer in the study of personality types. The personality typesare broadly defined accord to four main preferences. Do married couples choose similar ordifferent personality types in the mates? The following is the distribution of similarpreferences:

Number of Similar Preferencesl All four~

Three Two One {\J6'fJ

Probability .09 .35 .33 .19 ,,0

a. What is the probability that a married couple had no preferences in commonb. What is the probability that a married couple had no more than two preferenc U~,

common? ~~c. What is the probability that a married couple had at least two preferences in ~~

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Name two ways to make this calculation. ../71d. What is the probability that a married couple had either all four or no preferen 'e"'"

common? @~

Source Number of Jobs Obtainedfrom Source

Mass mailing 50Help-wanted ads 140Executive search firms 110

Networking 700

7. New spark plugs have just been installed in a small airplane with a four-cylinder engine. Foreach spark plug, the probability that it is defective and will fail during its first 20 minutes offlight is 1/10,000, independent of the other spark plugs..........

a. For any given spark plug, what is the probability thai it will not fail during the first 20

minutes of flight? '2.\)'

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b. What is the probability that none of the four spark plugs will fail during the first 20

minutes offlight? . 9'1'14)'1 =( . q<1<t0- " ~

c, What is the probability that at least one of the spark plugs win f~il?

, - - qeqq {g -,r (f ODOVd. If a plane rental company has 25 of these small ~rplanes-,"wh~tis the probability that

at least one of the spark plugs will fail?

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~8. A Psychological test identifies people as being one of eight types. For instance, Type I is

"Rationalist" and applies to 15% of men and 8% of women. Type 2 is "Teacher"and applies,to 12% of men and 14%,ofwomen. Each person fits one and only one_~: (c\isjo \ ('\+ J

a. What is the probability that a randomly selected male is either "Rationalist" or"Teacher"? /~;;1\

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.\'5+.12 ~~b. Whatis the probabilitythat a randoIIlly,sel!;~ed~ is not a "Teache~'?

f- ,Il.{ ~ (. '6~~c. Suppose college roommates 'have a~arlY hard time getting along with each

other if they are both "Ratio,!lalist." A college randomly assigns roommates of the- -",----same sex. What prOportionof male roommate pairs will have this problem? Of --'" """"""~"female roommate pairs? --

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d. IfJ!~lfgfJh~f911~g~i~_male and half female, what percent of al mate pairs willbe both "Rationali

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9. Jeanie is a bit forgetful, and if she doesn't make a "to do" list, the probability that she forgetssomething she is supposed to do is .1. Tomorrow she intends to run three errands, and shefails to write them on her list.

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a. What is the probability that Jeanie forgets all three errands?

, S - ~ '\ I \. -. v...,'- -b. What is the probability that Jeanie remembers at least one of the three errands?

(- . 001 ~ .qQ':.~)c. What is the probability that Jeanie remembers the first errand but not the second or

third? - q\ (, fj liJ , . -=. , ODD '\7 '-- ~

10. Find the probability that at least 1 of 5 fellow employees in San Francisco has a listednumber. Assume that terspn-~iifrers are independent and that for San Francisco, 39.5%of the numbers are unlisted.

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11. The IRS reports that among all taxpayers audited, 70% end up owing more money. One newauditor randomly selected 12 tax returns, audited them, and boasted that he collectedaclnltlon::tlt::txe~fTomall of them.

,~ 'Ia. What is the probability of accomplismng tills feat? L . ,.., ) (". D 13b. What is the probability that actually none of them owed money? :z .', "

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c. What is the probability that at least one of them did not owe money?-. ~, ,\ 6' J'.p' )

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