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 not independent events because P times open paren Z divides B close paren is not 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 independent events because P times open paren Z divides B close paren is equal to P times Z .
2
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How many patients had allergies or ear infections, but not both?

A
40
B
24
C
36
D
27
3

Which combination represents the empty set?

A
the intersection of motor and bicycle
B
the union of motor and bicycle
C
the union of motor and manual
D
the intersection of motor and manual
4

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 A divides cap c close paren is equal to 2 thirds
C
cap p times open paren cap b divides cap A close paren is equal to 13 over 27
D
cap p times open paren cap c divides cap b close paren is equal to 8 over 27
E
cap p times cap A is equal to 31 over 59
5

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 ninths
C
1 half
D
2 thirds
6

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 buys lunch divides male close paren is equal to cap p times male is equal to 0 point 4 .
D
cap p times open paren male divides buys lunch close paren is equal to cap p times male is equal to 0 point 3 .
7

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
40 percent
B
25 percent
C
67 percent
D
33 percent
8

To the nearest whole percent, what is the probability that a randomly selected customer from Satellite Company cap y watches recorded shows more often than live television?

A
59 percent
B
41 percent
C
83 percent
D
77 percent
9

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 a shaded portion and landing on an even number
C
landing on a shaded portion and landing on a number greater than 3
D
landing on a shaded portion and landing on a 3
E
landing on an unshaded portion and landing on an odd number
10

To the nearest tenth, what is the value of cap p times open paren cap c divides cap y close paren ?

A
0 point 5
B
0 point 4
C
0 point 8
D
0 point 7
11

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

A
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 .
B
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 .
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 1 6 and cap p times cap A is equal to 0 point 7 5 .
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 .
12

In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red. If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

A
1 eighth
B
3 fourths
C
2 thirds
D
1 half
13

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

A
60 comma 480
B
362 comma 874
C
3
D
6
14

Will surveyed students at his school about whether they have ever gone snowboarding and whether they own a skateboard. He found that 35 of the 99 students who own a skateboard have snowboarded. Also, there were 13 students who have snowboarded but do not own a skateboard, and 147 students who have never gone snowboarding and do not own a skateboard. Which two-way table correctly displays these data?

A
Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '13'; Column 4, '48' Row 3: Column 1, 'No Skateboard'; Column 2, '99'; Column 3, '147'; Column 4, '246' Row 4: Column 1, 'Total'; Column 2, '134'; Column 3, '160'; Column 4, '294'
B
Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '13'; Column 4, '48' Row 3: Column 1, 'No Skateboard'; Column 2, '64'; Column 3, '147'; Column 4, '211' Row 4: Column 1, 'Total'; Column 2, '99'; Column 3, '160'; Column 4, '256'
C
Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '64'; Column 4, '99' Row 3: Column 1, 'No Skateboard'; Column 2, '13'; Column 3, '147'; Column 4, '160' Row 4: Column 1, 'Total'; Column 2, '48'; Column 3, '211'; Column 4, '259'
D
Table with 4 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Have Snowboarded'; Column 3, 'Never Snowboarded'; Column 4, 'Total' Row 2: Column 1, 'Skateboard'; Column 2, '35'; Column 3, '99'; Column 4, '134' Row 3: Column 1, 'No Skateboard'; Column 2, '13'; Column 3, '147'; Column 4, '160' Row 4: Column 1, 'Total'; Column 2, '48'; Column 3, '246'; Column 4, '294'
15

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
4
B
3
C
2
D
1
16

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 1 5
B
0 point 3 0
C
0 point 0 9
D
0 point 6 0
17

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 he has fewer members on each team than Miguel’s does.
C
Miguel’s club has more possible team combinations because there are fewer members in his club.
D
Brent’s club has more possible team combinations because there are more members to choose from.
18

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

A
cap A is a strict subset of cap b
B
cap b to the c th power is equal to cap A
C
cap A to the c th power is equal to cap b
D
cap b is a strict subset of cap A
19

Consider cap u is equal to x divides x is A positive integer greater than 1 Which is an empty set?

A
start set x such that x is in cap u and 1 half x can be written as A fraction end set
B
start set x such that x is in cap u and 1 half x is prime end set
C
start set x such that x is in cap u and 2 x can be written as A fraction end set
D
start set x such that x is in cap u and 2 x is prime end set
20

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 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 .
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 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 .

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