Statistics and Probability, NAPX-J4-CA24 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

684

Question

Fifty football fans were surveyed about modes of transport they took to get to the game.

  • 22 caught a train
  • 21 caught a bus
  • 20 didn't take a train or a bus.

The diagram is missing some information.



How many caught both a train and a bus to get to the game?

Worked Solution

Interpreting the Venn diagram:

Since fifty fans surveyed,

  • 20 didn't take either train or bus
  • 9 caught train only
  • 8 caught bus only

∴\therefore Number that took both train and bus
= 50 − (20+9+8)50\ −\ (20 + 9 + 8)
= 13

Question Type

Answer Box

Variables

Variable nameVariable value
question
Fifty football fans were surveyed about modes of transport they took to get to the game. * 22 caught a train * 21 caught a bus * 20 didn't take a train or a bus. The diagram is missing some information.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-J4-CA24.svg 250 indent3 vpad
How many caught both a train and a bus to get to the game?
workedSolution
Interpreting the Venn diagram: sm_nogap Since fifty fans surveyed, * 20 didn't take either train or bus * 9 caught train only * 8 caught bus only sm_nogap $\therefore$ Number that took both train and bus
>>| | | ---------- | | \= $50\ −\ (20 + 9 + 8)$ | | \= {{{correctAnswer0}}} |
correctAnswer0
13
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer013

Variant 1

DifficultyLevel

686

Question

Eighty students were surveyed about instruments they play.

  • 39 play the piano
  • 18 play the guitar
  • 30 didn't play either instrument

The diagram is missing some information.



How many students play both the piano and the guitar?

Worked Solution

Interpreting the Venn diagram:

Since eighty students surveyed,

  • 30 didn't play either piano or guitar
  • 32 play piano only
  • 11 play guitar only

∴\therefore Number that play both piano and guitar
= 80 − (30+32+11)80\ −\ (30 + 32 + 11)
= 7

Question Type

Answer Box

Variables

Variable nameVariable value
question
Eighty students were surveyed about instruments they play. * 39 play the piano * 18 play the guitar * 30 didn't play either instrument The diagram is missing some information.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Stat_Prob_NAPX-J4-CA24-SA_v1.svg 250 indent3 vpad
How many students play both the piano and the guitar?
workedSolution
Interpreting the Venn diagram: sm_nogap Since eighty students surveyed, * 30 didn't play either piano or guitar * 32 play piano only * 11 play guitar only sm_nogap $\therefore$ Number that play both piano and guitar
>>| | | ---------- | | \= $80\ −\ (30 + 32 + 11)$ | | \= {{{correctAnswer0}}} |
correctAnswer0
7
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer07

Variant 2

DifficultyLevel

688

Question

Ninety six athletes were surveyed about the physiotherapist they had used during the season.

  • 45 used physio 1
  • 30 used physio 2
  • 26 didn't use a physio

The diagram is missing some information.



How many athletes used both physio 1 and physio 2?

Worked Solution

Interpreting the Venn diagram:

Ninety six athletes surveyed (given)

  • 26 didn't use physio 1 or physio 2
  • 40 used physio 1 only
  • 25 used physio 2 only

∴\therefore Number that used both physio 1 and 2
= 96 − (26+40+25)96\ −\ (26 + 40 + 25)
= 5

Question Type

Answer Box

Variables

Variable nameVariable value
question
Ninety six athletes were surveyed about the physiotherapist they had used during the season. * 45 used physio 1 * 30 used physio 2 * 26 didn't use a physio The diagram is missing some information.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Stat_Prob_NAPX-J4-CA24-SA_v2.svg 250 indent3 vpad
How many athletes used both physio 1 and physio 2?
workedSolution
Interpreting the Venn diagram: sm_nogap Ninety six athletes surveyed (given) * 26 didn't use physio 1 or physio 2 * 40 used physio 1 only * 25 used physio 2 only sm_nogap $\therefore$ Number that used both physio 1 and 2
>>| | | ---------- | | \= $96\ −\ (26 + 40 + 25)$ | | \= {{{correctAnswer0}}} |
correctAnswer0
5
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer05

Variant 3

DifficultyLevel

690

Question

Eighty eight shoppers at a department store were surveyed about the perfume they like.

  • 27 liked perfume 1
  • 33 liked perfume 2
  • 37 didn't like either perfume

The diagram is missing some information.



How many shoppers liked both the perfume A and perfume B?

Worked Solution

Interpreting the Venn diagram:

Eighty eight shoppers were surveyed (given)

  • 37 didn't like either perfume 1 or perfume 2
  • 18 liked perfume 1 only
  • 24 liked perfume 2 only

∴\therefore Number that like both perfume 1 and perfume 2
= 88 − (37+18+24)88\ −\ (37 + 18 + 24)
= 9

Question Type

Answer Box

Variables

Variable nameVariable value
question
Eighty eight shoppers at a department store were surveyed about the perfume they like. * 27 liked perfume 1 * 33 liked perfume 2 * 37 didn't like either perfume The diagram is missing some information.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Stat_Prob_NAPX-J4-CA24-SA_v3.svg 300 indent3 vpad
How many shoppers liked both the perfume A and perfume B?
workedSolution
Interpreting the Venn diagram: sm_nogap Eighty eight shoppers were surveyed (given) * 37 didn't like either perfume 1 or perfume 2 * 18 liked perfume 1 only * 24 liked perfume 2 only sm_nogap $\therefore$ Number that like both perfume 1 and perfume 2
>>| | | ---------- | | \= $88\ −\ (37 + 18 + 24)$ | | \= {{{correctAnswer0}}} |
correctAnswer0
9
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer09

Variant 4

DifficultyLevel

690

Question

Two hundred people were surveyed about the fruits they like.

  • 73 like bananas
  • 60 like apples
  • 83 didn't like either bananas or apples

The diagram is missing some information.



How many people like both bananas and apples?

Worked Solution

Interpreting the Venn diagram:

Two hundred people were surveyed (given)

  • 83 didn't like either bananas or apples
  • 57 like bananas only
  • 44 like apples only

∴\therefore Number that like both bananas and apples
= 200 − (57+44+83)200\ −\ (57 + 44 + 83)
= 16

Question Type

Answer Box

Variables

Variable nameVariable value
question
Two hundred people were surveyed about the fruits they like. * 73 like bananas * 60 like apples * 83 didn't like either bananas or apples The diagram is missing some information.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Stat_Prob_NAPX-J4-CA24-SA_v4.svg 300 indent3 vpad
How many people like both bananas and apples?
workedSolution
Interpreting the Venn diagram: sm_nogap Two hundred people were surveyed (given) * 83 didn't like either bananas or apples * 57 like bananas only * 44 like apples only sm_nogap $\therefore$ Number that like both bananas and apples
>>| | | ---------- | | \= $200\ −\ (57 + 44 + 83)$ | | \= {{{correctAnswer0}}} |
correctAnswer0
16
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer016

Variant 5

DifficultyLevel

682

Question

Three hundred people were surveyed about the movie cinemas they have attended in the last 6 months.

  • 160 have attended Events
  • 140 have attended Hoyts
  • 50 didn't attend either cinema

The diagram is missing some information.



How many people had attended both Events and Hoyts cinemas?

Worked Solution

Interpreting the Venn diagram:

Three hundred people were surveyed (given)

  • 50 didn't attend either Events or Hoyts
  • 110 attended Events only
  • 90 attended Hoyts only

∴\therefore Number that attended both Events and Hoyts
= 300 − (50+110+90)300\ −\ (50 + 110 + 90)
= 50

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three hundred people were surveyed about the movie cinemas they have attended in the last 6 months. * 160 have attended Events * 140 have attended Hoyts * 50 didn't attend either cinema The diagram is missing some information.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Stat_Prob_NAPX-J4-CA24-SA_v5.svg 300 indent3 vpad
How many people had attended both Events and Hoyts cinemas?
workedSolution
Interpreting the Venn diagram: sm_nogap Three hundred people were surveyed (given) * 50 didn't attend either Events or Hoyts * 110 attended Events only * 90 attended Hoyts only sm_nogap $\therefore$ Number that attended both Events and Hoyts
>>| | | ---------- | | \= $300\ −\ (50 + 110 + 90)$ | | \= {{{correctAnswer0}}} |
correctAnswer0
50
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer050

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