Answers AL-Algebra I with Probability Critical StandardsProbability and Two-Way Tables

Probability and Two-Way Tables — Unit test Answers

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Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination.If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?

504

3,024

60,480

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A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9. Each character in the password cannot be used more than once.What is the approximate probability that exactly one of the four characters will be a number?

11%

28%

44%

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?

0.00020

0.00476

0.06667

0.07142

A random number generator is used to create a list of 300 single-digit numbers. Of those 300 numbers, 146 are odd and 154 are even. The number 8 was generated 22 times.What is the experimental probability of an even number other than 8 being generated? Write your answer as a decimal to the nearest hundredths place.

0.23

0.35

0.44

0.52

Consider U = {x|x is a positive integer greater than 1}.Which is an empty set?

{x|x ∈ U and is prime}

{x|x ∈ U and 2x is prime}

{x|x ∈ U and can be written as a fraction}

{x|x ∈ U and 2x can be written as a fraction}

0.23

0.35

0.44

0.52

The cable company is analyzing the data from two satellite television providers to determine whether their users spend more time watching live television or shows that have been recorded.Satellite Company X: 89 live, 430 recordedSatellite Company Y: 65 live, 94 recorded

41%

59%

77%

83%

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.

A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 64, 99. The third column is labeled never snowboarded with entries 13, 147, 160. The fourth column is labeled Total with entries 48, 211, 256.

A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 13, 48. The third column is labeled never snowboarded with entries 99, 147, 246. The fourth column is labeled Total with entries 134, 160, 294.

A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 13, 48. The third column is labeled never snowboarded with entries 64, 147, 211. The fourth column is labeled Total with entries 99, 160, 259.

A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 99, 134. The third column is labeled never snowboarded with entries 13, 147, 160. The fourth column is labeled Total with entries 48, 246, 294.

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

A = {6}

A = {1, 3, 5, 7}

A = {1, 2, 3, 4, 5, 7, 8}

A = {1, 2, 3, 4, 5, 6, 7, 8}

Find P(C|Y) from the information in the table.

0.4

0.5

0.7

0.8

The diagram shows the number of children who have ever used motorized scooters, manual scooters, and/or bicycles.

motor ⋃ manual

motor ⋃ bicycle

motor ∩ manual

motor ∩ bicycle

Which probabilities are correct? Select two options.

P(A|C) =

P(C|B) =

P(A) =

P(C) =

P(B|A) =

Consider the sets below.A {x|x is a polygon}B {x|x is a triangle}Which is true?

A ⊂ B

B ⊂ A

Ac = B

Bc = A

A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 10, 110, 60, 180. The third column is labeled Y with entries 80, 44, 59, 183. The fourth column is labeled Z with entries 61, 126, 110, 297. The fifth column is labeled Total with entries 151, 280, 229, 660.

Z and B are independent events because P(Z∣B) = P(Z).

Z and B are independent events because P(Z∣B) = P(B).

Z and B are not independent events because P(Z∣B) ≠ P(Z).

Z and B are not independent events because P(Z∣B) ≠ P(B).

James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.Bring lunch: 46 males, 254 femalesBuy lunch: 176 males, 264 females

P(buys lunch | male) = P(male) = 0.4.

P(male | buys lunch) = P(male) = 0.3.

P(buys lunch | male) = 0.3 and P(male) = 0.4.

P(male | buys lunch) = 0.4 and P(male) = 0.3.

Bart found 20 quadrilaterals in his classroom. He made a Venn diagram using the properties of the quadrilaterals, comparing those with four equal side lengths (E) and those with four right angles (R).

25%

33%

40%

67%

A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive.What is true about spinning the spinner one time? Select three options.S = {1, 2, 3, 4, 5, 6, 7, 8}If A is a subset of S, A could be {1, 2, 3}.If A is a subset of S, A could be {7, 8, 9}.If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}.If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.

S = {1, 2, 3, 4, 5, 6, 7, 8}

If A is a subset of S, A could be {1, 2, 3}.

If A is a subset of S, A could be {7, 8, 9}.

If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}.

If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.

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?

The probability that Christina will choose three comedies can be expressed as .

The probability that Christina will choose three action movies can be expressed as .

The probability that Christina will not choose all comedies can be expressed as 1 − .

The probability that Christina will not choose all action movies can be expressed as 1 − .

The Venn diagram shows the number of patients seen at a pediatrician’s office in one week for colds, C, ear infections, E, and allergies, A.

Alejandro surveyed his classmates to determine who has ever gone surfing and who has ever gone snowboarding. Let A be the event that the person has gone surfing, and let B be the event that the person has gone snowboarding.

A and B are independent events because P(A∣B) = P(A) = 0.16.

A and B are independent events because P(A∣B) = P(A) = 0.75.

A and B are not independent events because P(A∣B) = 0.16 and P(A) = 0.75.

A and B are not independent events because P(A∣B) = 0.75 and P(A) = 0.16.

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Probability and Two-Way Tables — Unit test Answers

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