SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

  • Login
  • Get Help
  • About

Probability, NAP-K4-CA29

Pedro has 180 students in his year at school.

He surveys 30 students at random and asks them their favourite subject at school.

This column graph shows the results of the survey.
 

 
Which is the best estimate for the total number of students in Pedro's year whose favourite subject is English?

6 18 24 36 60
 
 
 
 
 
Show Answers Only

`18`

Show Worked Solution

`text(30 students surveyed out of 180)`

`=>\ text(1 in 6 surveyed)`

`:.\ text(Expected number who prefer English)`

`= 3 xx 6`

`= 18`

Filed Under: Probability, Probability Tagged With: Band 8, smc-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-K4-CA04

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?

 
 
 
 
Show Answers Only

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-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-J4-CA34 SA

Phil throws darts at a board split into 4 sections and records which section they hit.
 

 
Based on Phil's data, what is the probability that a dart he throws will land in section 2 or 3?

Express your answer as a percentage rounded to the nearest tenth.

 %
Show Answers Only

`text(89.4%)`

Show Worked Solution
`text(Number of throws)` `= 13 + 78 + 48 + 2`
  `= 141`

 

`:.\ text(Probability)` `= (78 + 48)/141`
  `= 126/141`
  `= 0.8936`
  `= 89.4text(%)`

Filed Under: Probability, Probability Tagged With: Band 10, smc-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-J4-CA10

Petunia picks a marble from a bag and records its colour before placing it back in the bag.

She repeats this 36 times.

Her results are in the table below.
 

   
 
Using the table, what is the probability that the next marble Petunia picks will be red?

`1/3` `1/6` `1/12` `1/4`
 
 
 
 
Show Answers Only

`1/4`

Show Worked Solution
`text{Pr(Red)}` `= text(number of reds picked)/text(total picks)`
  `= 9/36`
  `= 1/4`

Filed Under: Probability, Probability Tagged With: Band 8, smc-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-B4-NC15

Nev spins the arrow 50 times.

 

Which table is most likely to show the result?

 
 
 
 
Show Answers Only

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-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-C4-CA26

Wally asked all Year 9 students at his school what their favourite sport was.

He recorded the results in a table.
 

 
Which sport did 4 out of every 10 Year 9 students choose as their favourite?

`text(Water polo)` `text(Tennis)` `text(Cricket)` `text(Surfing)`
 
 
 
 
Show Answers Only

`text(Cricket)`

Show Worked Solution
`text(Total students)` `= 15 + 45 + 60 + 30`
  `= 150`

 
`text(Number of students needed)`

`= 4/10 xx 150`

`= 60`
 

`:. 4\ text(out of 10 chose cricket.)`

Filed Under: Probability, Probability Tagged With: Band 10, smc-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-C4-CA16

A die in the shape of a rectangular prism has 6 faces with 1 to 6 dots.

Brian throws the die 1000 times to test it and records the outcomes.
 

 
What is the probability of throwing a six based on Brian's results?

`1/6` `1/40` `6/25` `12/500`
 
 
 
 
Show Answers Only

`6/25`

Show Worked Solution
`P(6)` `=240/1000`
  `=6/25`

Filed Under: Probability, Probability Tagged With: Band 8, smc-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-B3-NC31 SA

Jon spins each pointer 50 times.

 

Each time he added the numbers that the pointers landed on.

His results are shown below.

\begin{array} {|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Sum of numbers}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & \textbf{Total}\\
\hline
\rule{0pt}{2.5ex}\textbf{Number of spins}\rule[-1ex]{0pt}{0pt} & 1 & 2 & 3 & 6 & 8 & 9 & 7 & 5 & 4 & 4 & 1 & \textbf{50} \\
\hline
\end{array}

What percentage of the spins resulted in a sum of 9?

  %
Show Answers Only

`text(10%)`

Show Worked Solution
`text(Percentage)` `= text(number of 9’s)/text(number of spins) xx 100`
  `=5/50 xx 100`
  `=10 text(%)`

Filed Under: Probability, Probability Tagged With: Band 10, smc-3191-30-Multi-step events, smc-3191-40-Relative frequency, smc-682-30-Multi-step events, smc-682-40-Relative frequency

Probability, NAP-G4-NC26

The table below shows all the people at Angus' birthday party.
 

What fraction of the children at the party are female?

`20/45` `20/60` `45/60` `20/100` `45/100`
 
 
 
 
 
Show Answers Only

`20/60`

Show Worked Solution

`text(Fraction of the children that are female)`

`= text(Female Children) / text(Total Children)`

`=20/60`

Filed Under: Probability, Probability Tagged With: Band 9, smc-3191-40-Relative frequency, smc-682-40-Relative frequency

Probability, NAP-G4-CA02

Arun flips an unbiased coin 200 times.

Which result is most likely?

`20\ text(tails)` `98\ text(tails)` `108\ text(tails)` `196\ text(tails)`
 
 
 
 
Show Answers Only

`98\ text(tails)`

Show Worked Solution

`text(The expected result is 100 tails.)`

`:.\ text(The most likely result is the one closest to 100 tails.)`

`=> 98\ text(tails)`

Filed Under: Probability, Probability Tagged With: Band 5, smc-3191-10-Core concepts, smc-3191-30-Multi-step events, smc-3191-40-Relative frequency, smc-682-10-Core concepts, smc-682-30-Multi-step events, smc-682-40-Relative frequency

Probability, NAP-I4-NC20

A group of 125 people were asked if they wear a watch or not.

This table shows the results.
 

 

A man was selected at random.

What is the probability that he wears a watch?

`0.20` `0.28` `0.32` `0.42`
 
 
 
 
Show Answers Only

`0.42` 

Show Worked Solution

`P(text(man wears watch))`

`= text(number of men wearing watch)/text(total men)`

`= 25/60`

`= 0.42`

Filed Under: Probability, Probability Tagged With: Band 8, smc-3191-40-Relative frequency, smc-682-40-Relative frequency

Copyright © 2014–2025 SmarterEd.com.au · Log in