Quiz 3 Basic Probability

8/13/2019 Quiz 3 Basic Probability

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Quiz 3 Basic probability

1. If the event of interest is A, then which of the following statements is correct?a. the probability that A will not occur is 1 !"A#

b. the probability that A will not occur is the probability of the complement of A

c. the probability that A will occur is zero if event A is impossible$. the probability A will occur is one if event A is certain%e. all of the above statements are correct

&. 'hich of the following $efinitions is correct?a. an activity, which results in an outcome, is calle$ an event

b. the probability of an event is e(presse$ in $ecimal form ranging from )1 to *1%c. the sample space refers to all possible outcomes of an e(periment$. the probability that an event will occur is calle$ the e(perimente. an event is the combination of all possible outcomes

3. 'hich of the following statements is not correct?a. if only one of the two events A an$ B can occur, in other wor$s, the occurrence ofone e(clu$es the occurrence of the other event, then events A an$ B are mutuallye(clusive

b. if events A an$ B can occur at the same time, then A an$ B intersect%c. if event A $oes not occur, then its complement, +, will also not occur$. a union of two events "eg A or B# occurs when at least one of the two eventsoccurse. If all possible outcomes of an e(periment are represente$ in a set, the set isconsi$ere$ to be e(haustive

-. If a contingency table shows the gen$er an$ year of stu$y of BBusci stu$ents "iefirst year, secon$ year, thir$ year or fourth year# in your statistics class, which of thefollowing statements is/are true?a. the events 0male stu$ent an$ 0female stu$ent are mutually e(clusive events

b. because of the fact that your stats class is a BBusci course only, all the events aree(haustive, in other wor$s, each stu$ent must fall into one of the classificationsc. an e(ample for the intersection of events "eg A an$ B# woul$ be of male stu$entswho are in first year$. an e(ample for the union of events "eg A or B# woul$ be stu$ents who are femaleor in secon$ year

%e. all of the above statements are correct

2. wo events, A an$ B, are sai$ to be mutually e(clusive ifa. !"A 4 B# 5 1

b. !"B 4 A# 5 1c. !"A an$ B# 5 1%$. !"A an$ B# 5 6e. none of the above

7. wo events, A an$ B, are sai$ to be in$epen$ent if%a. !"A an$ B# 5 !"A#.!"B#

b. !"A an$ B# 5 !"A# * !"B#c. !"A 4 B# 5 !"B#


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$. !"B 4 A# 5 !"A#e. none of the above

8. 9ill in the missing wor$ in the following statement with one of the options liste$below :vents are ;;;;;;;;;;; when the occurrence of one event has no effect on

the probability that another event will occur.a. mutually e(clusive%b. in$epen$entc. e(haustive$. $epen$ente. simultaneous

is the ran$om variable, c is a constant, an$ refers to thevariance. 'hich of the following laws of variance is not correct?a. "c# 5 6

b. "> * c# 5 ">#%c. "> * c# 5 "># * c$. "c ># 5 c& ">#e. all of the above are correct

16. @ou are given the following !"A an$ :# 5 6.18, !"+ an$ :# 5 6.3&, !"A an$ # 56.18 an$ !"+ an$ # 5 6.3-. 'hich of the following statements about A an$ : iscorrect?a. A an$ : are mutually e(clusive an$ in$epen$ent

b. A an$ : are mutually e(clusive an$ $epen$entc. A an$ : are not mutually e(clusive but are in$epen$ent%$. A an$ : are not mutually e(clusive an$ are $epen$ente. one of the above statements is correct

11. @ou are given the following !"A an$ :# 5 6.&6, !"+ an$ :# 5 6.3&, !"A an$ # 56.12 an$ !"+ an$ # 5 6.33. 'hich of the following statements about A an$ : iscorrect?a. A an$ : are mutually e(clusive an$ in$epen$ent


1&. @ou are given the following !"A an$ :# 5 6.1=, !"+ an$ :# 5 6.3


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a. A an$ : are mutually e(clusive an$ in$epen$entb. A an$ : are mutually e(clusive an$ $epen$entc. A an$ : are not mutually e(clusive but are in$epen$ent%$. A an$ : are not mutually e(clusive an$ are $epen$ente. one of the above statements is correct

13. @ou are given the following !"A an$ :# 5 6.18, !"+ an$ :# 5 6.33, !"A an$ # 56.&6 an$ !"+ an$ # 5 6.3. 'hich of the following statements about A an$ : iscorrect?a. A an$ : are mutually e(clusive an$ in$epen$ent


1-. @ou are given the following !"A an$ :# 5 6.17, !"+ an$ :# 5 6.3&, !"A an$ # 5

6.1& an$ !"+ an$ # 5 6.-6. 'hich of the following statements about A an$ : iscorrect?a. A an$ : are mutually e(clusive an$ in$epen$ent


12. If !"A# 5 6.


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e. 6.12

1=. If !"A# 5 6.7, !"B# 5 6.3 an$ !"A4B# 5 6.2, what is !"A an$ B#?%a. 6.12

b. 6.-&

c. 6.&8$. 6.-)ray test is use$ to $etect a $isease that occurs, initially without any obvioussymptoms, in 3C of the population. he test has the following error rates 8C of

people who are $isease free have a positive result an$ &C of the people who have the$isease have a negative result. A large number of people are screene$ at ran$om usingthe test, an$ those with a positive result are e(amine$ further. 'hat proportion of

people with a negative result actually have the $isease?a. 6.=)ray test is use$ to $etect a $isease that occurs, initially without any obvioussymptoms, in 3C of the population. he test has the following error rates 8C of

people who are $isease free have a positive result an$ &C of the people who have the$isease have a negative result. A large number of people are screene$ at ran$om usingthe test, an$ those with a positive result are e(amine$ further. 'hat proportion of thetests con$ucte$ give incorrect results?a. 6.=


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probability that if the wife is watching television, the husban$ is also watchingtelevision.a. 6.78%b. 6.28c. 6.23

$. 6.82e. 6.-8

1&8. An a$vertising e(ecutive is stu$ying television)viewing habits of marrie$ menan$ women $uring prime time hours. En the basis of past viewing recor$s, thee(ecutive has $etermine$ that $uring prime time, husban$s are watching television76C of the time. It has also been $etermine$ that when the husban$ is watchingtelevision, 36C of the time the wife is also watching. 'hen the husban$ is notwatching television, -6C of the time the wife is watching television. 9in$ the

probability that if the wife is watching television, the husban$ is also watchingtelevision.

a. 6.78b. 6.28%c. 6.23$. 6.82e. 6.-8

1&


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136. An a$vertising e(ecutive is stu$ying television)viewing habits of marrie$ menan$ women $uring prime time hours. En the basis of past viewing recor$s, thee(ecutive has $etermine$ that $uring prime time, husban$s are watching television76C of the time. It has also been $etermine$ that when the husban$ is watchingtelevision, -6C of the time the wife is also watching. 'hen the husban$ is not

watching television, 36C of the time the wife is watching television. 9in$ theprobability that the wife is watching television in prime time.%a. 6.37

b. 6.32c. 6.3-$. 6.3&e. 6.3=

131. An a$vertising e(ecutive is stu$ying television)viewing habits of marrie$ menan$ women $uring prime time hours. En the basis of past viewing recor$s, thee(ecutive has $etermine$ that $uring prime time, husban$s are watching television

26C of the time. It has also been $etermine$ that when the husban$ is watchingtelevision, -6C of the time the wife is also watching. 'hen the husban$ is notwatching television, 36C of the time the wife is watching television. 9in$ the

probability that the wife is watching television in prime time.a. 6.37%b. 6.32c. 6.3-$. 6.3&e. 6.3=

13&. An a$vertising e(ecutive is stu$ying television)viewing habits of marrie$ menan$ women $uring prime time hours. En the basis of past viewing recor$s, thee(ecutive has $etermine$ that $uring prime time, husban$s are watching television76C of the time. It has also been $etermine$ that when the husban$ is watchingtelevision, 36C of the time the wife is also watching. 'hen the husban$ is notwatching television, -6C of the time the wife is watching television. 9in$ the

probability that the wife is watching television in prime time.a. 6.37

b. 6.32%c. 6.3-$. 6.3&

e. 6.3=

133. An a$vertising e(ecutive is stu$ying television)viewing habits of marrie$ menan$ women $uring prime time hours. En the basis of past viewing recor$s, thee(ecutive has $etermine$ that $uring prime time, husban$s are watching television76C of the time. It has also been $etermine$ that when the husban$ is watchingtelevision, -6C of the time the wife is also watching. 'hen the husban$ is notwatching television, &6C of the time the wife is watching television. 9in$ the


b. 6.32

c. 6.3-%$. 6.3&


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e. 6.3=

13-. An a$vertising e(ecutive is stu$ying television)viewing habits of marrie$ menan$ women $uring prime time hours. En the basis of past viewing recor$s, thee(ecutive has $etermine$ that $uring prime time, husban$s are watching television

-6C of the time. It has also been $etermine$ that when the husban$ is watchingtelevision, -6C of the time the wife is also watching. 'hen the husban$ is notwatching television, 36C of the time the wife is watching television. 9in$ the


b. 6.32%c. 6.3-$. 6.3&e. 6.3=

132. Accor$ing to a recent survey of A househol$s, the probability that the resi$ents

of a househol$ own two cars if their annual househol$ income is over F126,666 is


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$. 6.13e. 6.67

1-3. Accor$ing to a recent survey of A househol$s, the probability that the resi$entsof a househol$ own two cars if their annual househol$ income is over F126,666 is


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two cars. 'hat is the probability that the annual househol$ income is over F126,666if the resi$ents of a househol$ own two cars?a. 6.7=

b. 6.28%c. 6.21

$. 6.8-e. 6.88

1- G ?

a. 6.


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%c. 6. H 3#?%a. 6.32

b. 6.-2c. 6.3 H 3#?%a. 6.32

b. 6.-2c. 6.3 G ?a. 6.62

b. 6.16%c. 6.6-$. 6.12e. 6.&6

173. @ou are given the following probability $istribution p") 5 6.&, p"6# 5 6.12,p" 5 6.2 an$ p"-# 5 6.12. 'hat is !"> G ?a. 6.62

b. 6.16c. 6.6-%$. 6.12e. 6.&6

17-. @ou are given the following probability $istribution p") 5 6.62, p"6# 5 6.12,p" 5 6.7 an$ p"-# 5 6.&. 'hat is !"> G ?a. 6.62

b. 6.16c. 6.6-$. 6.12

%e. 6.&6


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172. @ou are given the following probability $istribution p") 5 6.&, p"6# 5 6.12,p" 5 6.7 an$ p"-# 5 6.62. 'hat is !"> H ?%a. 6.=2

b. 6.=6c. 6.=7

$. 6. H ?a. 6.=2

b. 6.=6c. 6.=7%$. 6.#?


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a. -.66%b. 3.76c. -.16$. 3.16e. -.36

18&. @ou are given the following probability $istribution p"1# 5 6.12, p"3# 5 6.&, p"2#5 6.7 an$ p"8# 5 6.62. 'hat is :">#?a. -.66

b. 3.76%c. -.16$. 3.16e. -.36

183. @ou are given the following probability $istribution p"1# 5 6.&, p"3# 5 6.12, p"2#5 6.22 an$ p"8# 5 6.1. 'hat is :">#?

a. -.66b. 3.76%c. -.16$. 3.16e. -.36

18-. @ou are given the following probability $istribution p"1# 5 6.62, p"3# 5 6.3, p"2#5 6.7 an$ p"8# 5 6.62. 'hat is :">#?a. -.66

b. 3.76c. -.16$. 3.16%e. -.36

182. @ou are given the following probability $istribution p"1# 5 6.&, p"3# 5 6.12, p"2#5 6.7 an$ p"8# 5 6.62. 'hat is ">#?%a. 3.66

b. 3.7-c. &.2=$. 3.3=e. 1.18

187. @ou are given the following probability $istribution p"1# 5 6.3, p"3# 5 6.12, p"2#5 6.2 an$ p"8# 5 6.62. 'hat is ">#?a. 3.66%b. 3.7-c. &.2=$. 3.3=e. 1.18

188. @ou are given the following probability $istribution p"1# 5 6.12, p"3# 5 6.&, p"2#5 6.7 an$ p"8# 5 6.62. 'hat is ">#?

a. 3.66b. 3.7-


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%c. &.2=$. 3.3=e. 1.18

18#?%a. 1.66

b. 6.86c. 1.6# 5 & an$ "@# 5 3, then "&> an$ @#is%a. 11

b. &6.c. 8$. 17e. 1=

1=7. If > an$ @ are ran$om variables with "># 5 & an$ "@# 5 3, then "&> an$&@# is


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a. 11%b. &6.c. 8$. 17e. 1=

1=8. If > an$ @ are ran$om variables with "># 5 1 an$ "@# 5 3, then "&> an$ @#isa. 11

b. &6.%c. 8$. 17e. 1=

1= an$ @ are ran$om variables with "># 5 1 an$ "@# 5 3, then "&> an$&@# is

a. 11b. &6.c. 8%$. 17e. 1=

1==. If > an$ @ are ran$om variables with "># 5 - an$ "@# 5 3, then "&> an$ @#isa. 11

b. &6.c. 8$. 17%e. 1=

&66. @ou are given the following probability $istribution p")1# 5 6.-, p" 5 6.1, p"3#5 6.3 an$ p"8# 5 6.&. 'hat is :"2> * ?%a. 1&.2

b. 11. * ?a. 1&.2

b. 11. ) 1#?a. 1#?a. 3.66

b. 1.


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&12. @ou are given the following probability $istribution p") 5 6.&, p"6# 5 6.12,p" 5 6.7 an$ p"-# 5 6.62. 'hat is "&> * 3#?%a. 1&.6

b. 17.-c. 16.1

$. 12.6e. * 3#?a. 1&.6

b. 17.-c. 16.1%$. 12.6e.

Quiz 3 Basic Probability

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