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Probability, NAP-K3-CA28

A school canteen has two different types of sandwiches.

There are 14 chicken sandwiches and 11 vegemite sandwiches.

The canteen sells one sandwich to each of the first five students in line at lunch time.

The table shows the type of sandwich the first five students buy.
 

 
Dom is next in line and asks for a sandwich but doesn't care which type.

What is the chance that Dom is given chicken sandwich?

`text(100%)` `text(60%)` `text(56%)` `text(0%)`
 
 
 
 
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`text(60%)`

Show Worked Solution

`Ptext{(chicken sandwich for Dom)}`

`= text(chicken sandwiches left)/text(total sandwiches left)`

`= (14 – 2)/20`

`= 0.6`

`= 60text(%)`

Probability, NAP-A3-NC08

Ryan has white and black marbles in his bag.

If he chooses one without looking he is likely, but not certain, to get a white marble.

Which is Ryan's bag?

 
 
 
 

​

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Show Worked Solution

`text(The 1st option gives a)\ \ 3/5\ \ text(chance for a)`

`text{white marble (likely but not certain).}`

Probability, NAP-D3-NC05

A spinner is spun once.
 

 

 
Each shape on the wheel has an equal chance.

What is the chance that the spinner lands on the triangle .

 
 `text(5 chances in 6)`
 
 `text(6 chances in 6)`
 
 `text(1 chance in 5)`
 
 `text(1 chance in 6)`
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`text(1 chance in 6)`

Show Worked Solution

`text(S)text(ince all shapes have an equal chance,)`​

`Ptext{(triangle)}` `= 1/6`

Probability, NAP-E3-NC25 SA

Sharon made 24 milkshakes at her nephew's birthday party. The milkshakes were either vanilla or chocolate.

All the milkshakes were served in an aluminium cup and looked the same.

Murray took one milkshake and had a 1 in 8 chance of taking a vanilla milkshake.

How many chocolate milkshakes did Sharon make?
Show Answers Only

`21`

Show Worked Solution

`text(Number of vanilla milkshakes)`

`= 1/8 xx 24`

`= 3`
 

`:.\ text(Number of chocolate)`

`= 24 – 3`

`= 21`

Probability, NAP-E3-NC16

Shane rolls a standard six-sided die.

Which of the following events has a probability of less than 0.5?

 
 rolling a number greater than 1
 
 rolling an odd number
 
 rolling a number less than 6
 
 rolling a number greater than or equal to 6
Show Answers Only

`text(rolling a number greater than or equal to 6)`

Show Worked Solution

`P(text(rolling a number) >= 6) = 1/6,`

`text(which is less than 0.5.)`

Probability, NAP-G3-NC16

Francis has a bag of marbles.

The number of marbles of each colour is recorded in the table below.
 

   

 
Francis randomly takes 1 marble out of her bag without looking.

What is the chance it is green?

`1/28` `1/7` `1/4` `1/2`
 
 
 
 
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`1/2`

Show Worked Solution
`text{Pr (Green)}` `= text(Number of green) / text(Total number)`
  `=14/28`
  `=1/2`

Probability, NAP-G3-CA05

Shane rolls a standard 6-sided dice once.

Which of the following is Shane most likely to roll?

 
 a number less than 3
 
 a number greater than 2
 
 an even number
 
 the number 3 or 4
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`text(a number greater than 2)`

Show Worked Solution

`text(Consider the probability of each option:)`

`P\ text{(a number less than 3)} = 2/6`

`P\ text{(a number greater than 2)} = 4/6`

`P\ text{(an even number)} = 1/2`

`P\ text{(3 or 4)} = 2/6`
 

`:.\ text(A number greater than 2 is most likely.)`

Probability, NAP-I3-CA18

Archer did a survey of his class, asking everyone what their favourite ice cream flavour is.

This table below shows the results.
 

   

 
What is the probability that a randomly selected classmate's favourite flavour is chocolate?

Round your answer to the nearest hundredth.

`0.15` `0.39` `0.48` `0.61`
 
 
 
 
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`0.39`

Show Worked Solution

`Ptext{(Classmate selected likes chocolate)}`

  `= text(number who chose chocolate) / text(total number of classmates)`
  `=15/(15+16+7)`
  `=15/38`
  `=0.39\ \ text{(nearest hundredth)}`

Probability, NAP-H3-CA17

Claire baked 18 cookies.

She baked equal numbers of chocolate chip, macadamia nut and plain cookies.

Claire randomly picked one of the cookies.

What are the chances it was chocolate chip or plain?

`2/18` `1/18` `10/18` `2/3` `1/3`
 
 
 
 
 
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`2/3`

Show Worked Solution

`P(text(choosing chocolate chip or plain))`

`= text(number of chocolate chip and plain)/text(total number of cookies)`

`= 12/18`

`= 2/3`

Probability, NAP-I3-CA07

Bellamy creates a game with the spinner shown below.
 

 
If the spinner lands on a 3, he wins a prize.

What is the probability that Bellamy will win a prize on his next spin?

`1/4`  `1/3`  `3/8`  `1/2`
 
 
 
 
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`1/4`

Show Worked Solution
`P text{(landing on a 3)}` `= text(Number of 3’s)/text(Total possibilities)`
  `=2/8`
  `=1/4`

Probability, NAP-I3-NC06 SA

Peter has a marble bag that contains 20 marbles that are either red or green in colour.

The probability of randomly picking a green marble is 70%.

What is the probability of randomly picking a red marble?

  %
Show Answers Only

`text(30%)`

Show Worked Solution
`P(text(green)) + P(text(red))` `= 100text(%)`
`text(70%)\ + P(text(red))` `= 100text(%)`
`:. P(text(red))` `= 30text(%)`