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Probability, NAP-L3-CA33 SA

Rachel has a bag that contains 6 blue and 4 green balls.

She selects one ball at random and records its colour. The ball is then put back into the bag.

Rachel does this 50 times.

How many times should Rachel expect to select a green ball from the bag?

 
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`20`

Show Worked Solution

`P(text(picking green)) = 4/10 = 2/5`

`:.\ text(Expected green balls)` `= 2/5 xx 50`
  `= 20`

Filed Under: Probability, Probability Tagged With: Band 9, smc-3167-40-Relative frequency, smc-675-40-Relative frequency

Probability, NAP-K3-CA09

Spiro spins the arrow of this spinner 40 times.

He records the number of times the arrow lands on each number.
 


 

Which table records the most likely results?

 
 
 
 
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Show Worked Solution

`text(Landing on 1 or 5 is approximately one-third chance)`

`text(which is 13 times.)`

`text(Landing on 4 is expected to occur slightly less often)`

`text(than landing on 2 or 3.)`

Filed Under: Probability, Probability Tagged With: Band 7, smc-3167-40-Relative frequency, smc-675-40-Relative frequency

Probability, NAP-J3-CA40 SA

A random sample of people were asked what their favourite winter sport was.

The table below recorded the results.
 

   

Using the data from the survey, predict how many people would choose rugby league if 2000 people were surveyed.

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`1250`

Show Worked Solution

`text(Total people surveyed)`

`= 49 + 19 + 135 + 13`

`= 216`

`:.\ text(Predicted number to choose rugby league)`

`= 135/216 xx 2000`

`= 1250`

Filed Under: Probability, Probability Tagged With: Band 10, smc-3167-40-Relative frequency, smc-675-40-Relative frequency

Probability, NAP-B3-NC17

Nev spins the arrow 50 times.
 

 

 
Which table is most likely to show his result?

 
 
 
 
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Show Worked Solution

`text(One strategy:)`

`X\ text{should be worth around 40% (20 spins),}`

`=>\ text(Eliminate the first and last options.)`

`text(The other relative sizes require the answer to be:)`

Filed Under: Probability, Probability Tagged With: Band 8, smc-3167-40-Relative frequency, smc-675-40-Relative frequency

Probability, NAP-C3-CA27

Mandy surveyed all year 7 students about their favourite flavour of milkshake.
 

   

 
Which flavour did 4 out of 10 year 7 students choose as their favourite?

`text(Chocolate)` `text(Vanilla)` `text(Strawberry)` `text(Caramel)`
 
 
 
 
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`text(Vanilla)` 

Show Worked Solution
`text(Total students)` `=75+100+35+40`
  `=250`

 
`text(If 4 out of 10 students chose a certain flavour,)`

`text(Number of students)`

`=40text(%) xx 250`

`=100`
 

`:.\ text(4 out of 10 students choose Vanilla.)` 

Filed Under: Probability, Probability Tagged With: Band 9, smc-3167-40-Relative frequency, smc-675-40-Relative frequency

Probability, NAP-G3-NC19

A spinner can land in any of 4 sections, labelled 1 to 4.

The spinner is spun 100 times and the results are recorded in the bar chart below.

 

 

Which of these spinners is most likely to give results shown in the graph?
 

 
 
 
 
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Show Worked Solution

`text(Landing on 3 should be about 50%.)`

`text(Landing on 4 should be about 25%.)`

`text{Landing on 1 and 2 (combined) should be about 25%.}`

 

Filed Under: Probability, Probability Tagged With: Band 7, smc-3167-40-Relative frequency, smc-675-40-Relative frequency

Probability, NAP-I3-NC24 SA

Ricky rolled a standard dice 80 times.

He recorded if an odd or even number was rolled, each time, and wrote the results in the table below.
 

   

What is the difference between the expected number of odd rolls and the actual number recorded?

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`3`

Show Worked Solution

`text(50% = the probability of an odd roll.)`

`text(Expected odd rolls)`

`= 50text(%) xx 80`

`= 40`
 

`:.\ text(Difference)` `= 40 – 37`
  `= 3`

Filed Under: Probability, Probability Tagged With: Band 8, smc-3167-40-Relative frequency, smc-675-40-Relative frequency

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