Statistics and Probability, NAPX-I4-CA19

Question

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Worked Solution

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Variant 0

DifficultyLevel

617

Question

Cedar surveyed 42 families about what brand of car they own.

The Venn diagram shows the results.

What is the probability that a family randomly selected from the group owns both a Toyota and a VW, rounded to three decimal places?

Worked Solution

PP(own both Toyota and VW)
= 642\dfrac{6}{42}
= 0.1428 …
= 0.143 (to 3 d.p.)

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Cedar surveyed 42 families about what brand of car they own. The Venn diagram shows the results. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-I4-CA19rev.svg 300 indent vpad What is the probability that a family randomly selected from the group owns both a Toyota and a VW, rounded to three decimal places?
workedSolution
sm_nogap $P$(own both Toyota and VW)
>| | | | ------------- | ---------- | | | \= $\dfrac{6}{42}$ | | | \= 0.1428 … | | | \= {{{correctAnswer}}} (to 3 d.p.) |
correctAnswer
0.143

Answers

Is Correct?Answer
x

0.381

x

0.310

x

0.231

x

0.167

✓

0.143

Variant 1

DifficultyLevel

615

Question

Ben surveyed 42 families about what brands of car they own.

The Venn diagram shows the results.

What is the probability that a family randomly selected from the group owns a Toyota, rounded to three decimal places?

Worked Solution

PP(owns a Toyota)
= 13+642\dfrac{13 + 6}{42}
= 1942\dfrac{19}{42}
= 0.4523...
= 0.452 (to 3 d.p.)

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Ben surveyed 42 families about what brands of car they own. The Venn diagram shows the results. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-I4-CA19rev.svg 300 indent vpad What is the probability that a family randomly selected from the group owns a Toyota, rounded to three decimal places?
workedSolution
sm_nogap $P$(owns a Toyota)
>| | | | ------------- | ---------- | | | \= $\dfrac{13 + 6}{42}$ | | | \= $\dfrac{19}{42}$ | | | \= 0.4523...| | | \= {{{correctAnswer}}} (to 3 d.p.) |
correctAnswer
0.452

Answers

Is Correct?Answer
x

0.190

x

0.310

x

0.356

x

0.448

✓

0.452

Variant 2

DifficultyLevel

618

Question

Imogen surveyed 42 families about what brands of car they own.

The Venn diagram shows the results.

What is the probability that a family randomly selected from the group owns a VW or a Toyota, but not both?

Worked Solution

PP(owns only a Toyota or VW)
= 13+742\dfrac{13 + 7}{42}
= 2042\dfrac{20}{42}
= 0.4761...
= 0.476 (to 3 d.p.)

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Imogen surveyed 42 families about what brands of car they own. The Venn diagram shows the results. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-I4-CA19rev.svg 300 indent vpad What is the probability that a family randomly selected from the group owns a VW or a Toyota, but not both?
workedSolution
sm_nogap $P$(owns only a Toyota or VW)
>| | | | ------------- | ---------- | | | \= $\dfrac{13 + 7}{42}$ | | | \= $\dfrac{20}{42}$ | | | \= 0.4761...| | | \= {{{correctAnswer}}} (to 3 d.p.) |
correctAnswer
0.476

Answers

Is Correct?Answer
x

0.143

✓

0.476

x

0.619

x

0.762

x

0.909

Tags