AnswersMathematics IIApplications of Probability

Applications of Probability — Test Answers

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1
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Which statement is true about whether Z and B are independent events?

A
Z and B are independent events because P times open paren Z divides B close paren is equal to P times Z .
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 B .
D
Z and B are not independent events because P times open paren Z divides B close paren is not equal to P times Z .
2
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Pedro has determined that the probability his shot will score in a lacrosse game is 0 point 3 0 What is the probability that he will score on two consecutive shots?

A
0 point 6 0
B
0 point 3 0
C
0 point 0 9
D
0 point 1 5
3

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
Brent’s club has more possible team combinations because he has fewer members on each team than Miguel’s does.
B
Brent’s club has more possible team combinations because there are more members to choose from.
C
Miguel’s club has more possible team combinations because he has more members on each team than Brent does.
D
Miguel’s club has more possible team combinations because there are fewer members in his club.
4

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 choose three comedies can be expressed as the fraction with numerator 1 and denominator sub 4 mathrm cap c sub 3 .
B
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 .
C
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 .
D
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 .
5

Evaluate the expression. the fraction with numerator 9 factorial and denominator 3 factorial

A
3
B
6
C
60 comma 480
D
362 comma 874
6

Aaron, Bob, and Charlotte are running a race. Which event would be considered dependent?

A
determining whose coach runs the stopwatch
B
determining the chance that Bob comes in first or third
C
determining which person begins on the inside lane
D
determining first, second, and third place runners
7

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
5 sixths times 3 sixths
B
1 sixth times 1 fifth
C
1 sixth times 1 sixth
D
1 fifth times 1 third
8

Consider the sets. cap A x divides x is a polygon cap b x divides x is a triangle Which is true?

A
cap b is a strict subset of cap A
B
cap A to the c th power is equal to cap b
C
cap A is a strict subset of cap b
D
cap b to the c th power is equal to cap A
9

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
10

Dependent events can best be described as

A
a group of events whose later outcomes are affected by previous outcomes.
B
two or more events that have the same probabilities.
C
a group of events whose later outcomes are not affected by previous outcomes.
D
two or more events that do not have the same probabilities.
11

Jillian has three different bracelets X, Y, and Z to give to her friends as gifts in any order she prefers. If bracelet cap y is chosen first, in how many ways can Jillian give out the bracelets?

A
3
B
2
C
4
D
1
12

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 c sub 1 close paren times open paren sub 9 cap c sub 3 close paren and denominator sub 10 cap c 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 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
D
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
13

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 cap A is a subset of cap s , cap A could be start set 1 comma 2 comma 3 end set .
B
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 .
C
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 .
D
If cap A is a subset of cap s , cap A could be start set 7 comma 8 comma 9 end set .
E
cap s is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8
14

A bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. Two marbles are drawn from the bag. What is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?

A
0 point 0 4 4 4 4
B
0 point 0 2 2 2 2
C
0 point 1 3 3 3 3
D
0 point 0 8 8 8 9
15

Four seniors and six juniors are competing for four places on a quiz bowl team. What is the approximate probability that all four seniors will be chosen at random?

A
0 point 0 0 4 7 6
B
0 point 0 7 1 4 2
C
0 point 0 0 0 2 0
D
0 point 0 6 6 6 7
16

Given that a randomly chosen quadrilateral has four right angles, what is the probability that the quadrilateral also has four equal side lengths? Express your answer in percent form, rounded to the nearest whole percent.

A
33 percent
B
40 percent
C
25 percent
D
67 percent
17

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 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 .
D
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 .
18

Which events are mutually exclusive? Choose two correct answers.

A
landing on a shaded portion and landing on an even number
B
landing on a shaded portion and landing on a 3
C
landing on an unshaded portion and landing on a number less than 2
D
landing on a shaded portion and landing on a number greater than 3
E
landing on an unshaded portion and landing on an odd number
19

What is the probability that the spinner will land on a number greater than 4 or on a shaded section?

A
5 sixths
B
2 thirds
C
1 half
D
2 ninths
20

Which probabilities are correct? Choose two correct answers.

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

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