AnswersGeometryApplications of Probability

Applications of Probability — Test Answers

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3

The events "male” and "buys lunch” are not independent because

A
cap p times open paren buys lunch divides male close paren is equal to 0 point 3 and cap p times male is equal to 0 point 4 .
B
cap p times open paren male divides buys lunch close paren is equal to 0 point 4 and cap p times male is equal to 0 point 3 .
C
cap p times open paren male divides buys lunch close paren is equal to cap p times male is equal to 0 point 3 .
D
cap p times open paren buys lunch divides male close paren is equal to cap p times male is equal to 0 point 4 .
5

Which probabilities are correct? Choose two correct answers.

A
cap p times open paren cap b divides cap A close paren is equal to 13 over 27
B
cap p times cap c is equal to 3 sevenths
C
cap p times open paren cap c divides cap b close paren is equal to 8 over 27
D
cap p times open paren cap A divides cap c close paren is equal to 2 thirds
E
cap p times cap A is equal to 31 over 59
7

Which statement is true about whether Z and B are independent events?

A
Z and B are not independent events because P times open paren Z divides B close paren is not equal to P times B .
B
Z and B are independent events because P times open paren Z divides B close paren is equal to P times B .
C
Z and B are not independent events because P times open paren Z divides B close paren is not equal to P times Z .
D
Z and B are independent events because P times open paren Z divides B close paren is equal to P times Z .
8

Which events are mutually exclusive? Choose two correct answers.

A
landing on an unshaded portion and landing on a number less than 2
B
landing on an unshaded portion and landing on an odd number
C
landing on a shaded portion and landing on a 3
D
landing on a shaded portion and landing on a number greater than 3
E
landing on a shaded portion and landing on an even number
9

Which statement is true about whether cap A and cap b are independent events?

A
cap A and cap b are independent events because cap p times open paren cap A divides cap b close paren is equal to cap p times cap A is equal to 0 point 1 6 .
B
cap A and cap b are not independent events because cap p times open paren cap A divides cap b close paren is equal to 0 point 1 6 and cap p times cap A is equal to 0 point 7 5 .
C
cap A and cap b are not independent events because cap p times open paren cap A divides cap b close paren is equal to 0 point 7 5 and cap p times cap A is equal to 0 point 1 6 .
D
cap A and cap b are independent events because cap p times open paren cap A divides cap b close paren is equal to cap p times cap A is equal to 0 point 7 5 .
11

Which combination represents the empty set?

A
the union of motor and manual
B
the union of motor and bicycle
C
the intersection of motor and bicycle
D
the intersection of motor and manual
12

Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. Which statement is true?

A
The probability that Christina will not choose all comedies can be expressed as 1 minus the fraction with numerator 4 cap c sub 3 and denominator 20 cap c sub 4 .
B
The probability that Christina will choose three comedies can be expressed as the fraction with numerator 1 and denominator sub 4 mathrm cap c sub 3 .
C
The probability that Christina will not choose all action movies can be expressed as 1 minus the fraction with numerator 9 cap c sub 3 and denominator 20 cap c sub 3 .
D
The probability that Christina will choose three action movies can be expressed as the fraction with numerator sub 20 mathrm cap c sub 3 and denominator sub 9 mathrm cap c sub 3 .
14

A security alarm requires a four-digit code. The code can use the digits 0 - 9 and the digits cannot be repeated. Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7 ?

A
the fraction with numerator open paren sub 10 cap p sub 1 close paren times open paren sub 9 cap p sub 3 close paren and denominator sub 10 cap p sub 4
B
the fraction with numerator open paren sub 2 cap c sub 1 close paren times open paren sub 9 cap c sub 3 close paren and denominator sub 10 cap c sub 4
C
the fraction with numerator open paren sub 2 cap p sub 1 close paren times open paren sub 9 cap p sub 3 close paren and denominator sub 10 cap p sub 4
D
the fraction with numerator open paren sub 10 cap c sub 1 close paren times open paren sub 9 cap c sub 3 close paren and denominator sub 10 cap c sub 4
15

Brent’s after-school game club has 12 members from which a six-member team is created. Miguel’s after-school sports club has 10 members from which a six-member team is created. Which student’s club has more possible combinations for his six-member team?

A
Miguel’s club has more possible team combinations because he has more members on each team than Brent does.
B
Brent’s club has more possible team combinations because there are more members to choose from.
C
Brent’s club has more possible team combinations because he has fewer members on each team than Miguel’s does.
D
Miguel’s club has more possible team combinations because there are fewer members in his club.
17

Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. Subset cap A of the sample space represents the complement of the event in which the number 6 is drawn from the bag. Which shows subset cap A ?

A
cap A is equal to 6
B
cap A is equal to 1 comma 3 comma 5 comma 7
C
cap A is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8
D
cap A is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 7 comma 8
19

A spinner is divided into eight equal-sized sections, numbered from 1 to 8 , inclusive. What is true about spinning the spinner one time? Choose three correct answers.

A
If a subset cap A represents spinning a number less than 4 ,then cap A is equal to 1 comma 2 comma 3 comma 4 .
B
If cap A is a subset of cap s , cap A could be start set 1 comma 2 comma 3 end set .
C
If cap A is a subset of cap s , cap A could be start set 7 comma 8 comma 9 end set .
D
cap s is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8
E
If a subset cap A represents the complement of spinning an odd number, then cap A is equal to 2 comma 4 comma 6 comma 8 .
20

A six-sided number cube is rolled twice. Which expression can be used to find cap p times open paren 5 comma then 3 close paren ?

A
1 sixth times 1 fifth
B
5 sixths times 3 sixths
C
1 sixth times 1 sixth
D
1 fifth times 1 third

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