SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Probability, SMB-015

On a tray there are 12 hard‑centred chocolates and 8 soft‑centred chocolates . Two chocolates are selected at random. A partially completed probability tree is shown.
 


 

What is the probability of selecting at least one soft-centred chocolate?  (3 marks)

Show Answers Only

Show Worked Solution

♦ Mean mark 45%.

Probability, SMB-014

A game consists of two tokens being drawn at random from a barrel containing 20 tokens. There are 17 red tokens and 3 black tokens. The player keeps the two tokens drawn.

  1.  Complete the probability tree by writing the missing probabilities in the boxes.  (2 marks)
     
     
       

  2.  What is the probability that a player draws at least one red token? Give your answer in exact form.  (2 marks)

Show Answers Only
  1.  
Show Worked Solution
i.   

 

ii.   

Probability, SMB-013

Beib owns three white and five blue T-shirts. He chooses a T-shirt at random for himself and puts it on. He then chooses another T-shirt at random, from the remaining T-shirts, and gives it to his brother.

  1. What is the probability that Beib chooses a blue T-shirt for himself?  (1 mark)

  2. Complete the tree diagram by writing the correct probability on each branch.  (2 marks)
     
         

  3. Calculate the probability that both of the T-shirts are the same colour.  (2 marks)

Show Answers Only
  2.  
Show Worked Solution

i.   

  
ii.    

       

 
iii. 

Probability, SMB-011

Tay-Tay has 2 bags of apples.

Bag A contains 4 red apples and 3 green apples. 

Bag B contains 3 red apples and 1 green apple.

Tay-Tay chooses one of the bags randomly and with her eyes closed, takes one of the apples. 

  1. Complete the tree diagram below.   (2 marks)
     

  2. Determine the probability that Tay-Tay chooses a red apple?   (2 marks) 

Show Answers Only

i.    
       

ii.   

Show Worked Solution

i.    
       
 

ii.    
   

Probability, SMB-006

Bromley rolls two standard dice at the same time and adds up the total.

 An incomplete table of the possible outcomes is below.

  1. Complete the table.   (2 marks)

  2. What is the most likely total that Bromley will roll?   (1 mark)

Show Answers Only

i.

ii.   

Show Worked Solution

i.

 
ii.   

Probability, SMB-002

A representative soccer team is chosen from 30 players who play for two clubs, Portland and Lithgow.

10 players from Portland and 20 players from Lithgow are playing in the trials, and 7 players from Portland and 8 from Lithgow are selected in the representative team.
 

 
One player at the trial is randomly selected.

What is the probability that the player is from Lithgow and is selected in the representative team?

Give your answer to two decimal places.   (2 marks)

Show Answers Only

Show Worked Solution

Probability, SMB-001

A coin is tossed 3 times. There are 8 possible outcomes.

What is the probability of getting 2 heads and 1 tail in any order?   (2 marks)

Show Answers Only

Show Worked Solution


 

  1st toss H H H H T T T T
  2nd toss H H T T H H T T
  3rd toss H T H T H T H T
       ✓  ✓    ✓      


  


 

Probability, STD2 S2 2019 HSC 25

A bowl of fruit contains 17 apples of which 9 are red and 8 are green.

Dennis takes one apple at random and eats it. Margaret also takes an apple at random and eats it.

By drawing a probability tree diagram, or otherwise, find the probability that Dennis and Margaret eat apples of the same colour.  (3 marks)

Show Answers Only

Show Worked Solution

 
 
 
♦♦ Mean mark 35%.

Probability, STD2 S2 2005 HSC 23a

There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The number of tickets she sold to each friend is shown in the table.
 

  1. Justine claims that each of her friends is equally likely to win first prize.

     

    Give a reason why Justine’s statement is NOT correct.   (1 mark)

  2. What is the probability that first prize is NOT won by Khalid or Herman?   (2 marks)

Show Answers Only


Show Worked Solution

i.   

 

ii. 


 

Probability, STD2 S2 2007 HSC 25c

In a stack of 10 DVDs, there are 5 rated PG, 3 rated G and 2 rated M.

  1. A DVD is selected at random. What is the probability that it is rated M?   (1 mark)

Grant chooses two DVDs at random from the stack. Copy or trace the tree diagram into your writing booklet.
 

  1. Complete the tree diagram by writing the correct probability on each branch.   (2 marks)

  2. Calculate the probability that Grant chooses two DVDs with the same rating.   (2 marks)

Show Answers Only
  2.  
Show Worked Solution

i.   

 

 

ii.   

 

iii. 

Probability, STD2 S2 2014 HSC 16 MC

In Mathsville, there are on average eight rainy days in October.

Which expression could be used to find a value for the probability that it will rain on two consecutive days in October in Mathsville?

Show Answers Only

Show Worked Solution

♦♦♦ Mean mark 16%.
Lowest mark of any MC question in 2014!

Probability, STD2 S2 2009 HSC 27c

In each of three raffles, 100 tickets are sold and one prize is awarded.

Mary buys two tickets in one raffle. Jane buys one ticket in each of the other two raffles.

Determine who has the better chance of winning at least one prize. Justify your response using probability calculations.   (4 marks)  

Show Answers Only
 

 

 
 
 

 

Show Worked Solution
 

 

 
 
 

 

♦♦ Mean mark 31%.
MARKER’S COMMENT: Very few students calculated Jane’s chance of winning correctly. Note the use of “at least” in the question. Finding (complement) is the best strategy here.

Probability, STD2 S2 2013 HSC 26c

The probability that Michael will score more than 100 points in a game of bowling is . 

  1. A commentator states that the probability that Michael will score less than 100 points in a game of bowling is  .

     

    Is the commentator correct? Give a reason for your answer.   (1 mark)

  2. Michael plays two games of bowling. What is the probability that he scores more than 100 points in the first game and then again in the second game?   (1 mark)

Show Answers Only
Show Worked Solution
♦♦♦ Mean mark 11%

i.  

 

♦ Mean mark 34%
ii.  
   

Probability, STD2 S2 2010 HSC 20 MC

Lou and Ali are on a fitness program for one month. The probability that Lou will finish the program successfully is 0.7 while the probability that Ali will finish successfully is 0.6. The probability tree shows this information

 

What is the probability that only one of them will be successful ?

Show Answers Only

Show Worked Solution

 
 
 

 

♦ Mean mark 48%.

Probability, STD2 S2 2012 HSC 27e

A box contains 33 scarves made from two different fabrics. There are 14 scarves made from silk (S) and 19 made from wool (W).
Two girls each select, at random, a scarf to wear from the box.

  1. Complete the probability tree diagram below.   (2 marks) 
      
       

  2. Calculate the probability that the two scarves selected are made from silk.    (1 mark)

  3. Calculate the probability that the two scarves selected are made from different fabrics.   (2 marks)

Show Answers Only
  1.  
       
     
Show Worked Solution

i. 

♦ Mean mark (i) 43%.
ii. 
 
 

 

iii. 
 
 
 
♦ Mean mark (iii) 41%.
MARKER’S COMMENT: In better responses, students multiplied along the branches and then added these two results together

Probability, STD2 S2 2013 HSC 18 MC

Two unbiased dice, each with faces numbered  1, 2, 3, 4, 5, 6,  are rolled.

What is the probability of obtaining a sum of 6?

Show Answers Only

Show Worked Solution

♦♦ Mean mark 35%.