On a tray there are 12 hard‑centred chocolates
What is the probability of selecting at least one soft-centred chocolate? (3 marks)
--- 7 WORK AREA LINES (style=lined) ---
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.
- Complete the probability tree by writing the missing probabilities in the boxes. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- What is the probability that a player draws at least one red token? Give your answer in exact form. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Show Answers Only
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.
- What is the probability that Beib chooses a blue T-shirt for himself? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Complete the tree diagram by writing the correct probability on each branch. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- Calculate the probability that both of the T-shirts are the same colour. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Show Answers Only
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.
- Complete the tree diagram below. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- Determine the probability that Tay-Tay chooses a red apple? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
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)
--- 4 WORK AREA LINES (style=lined) ---
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)
--- 5 WORK AREA LINES (style=lined) ---
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)
--- 8 WORK AREA LINES (style=lined) ---
Show Worked Solution
♦♦ Mean mark 35%.
Probability, STD2 S2 2016 HSC 28c
A cricket team is about to play two matches. The probability of the team having a win, a loss or a draw is 0.7, 0.1 and 0.2 respectively in each match. The possible results in the two matches are displayed in the probability tree diagram.
- What is the probability of the team having a win and a draw, in any order? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Paul claims that 1.4 is the probability of the team winning both matches.
Give one reason why this is NOT correct. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Probability, STD2 S2 2007 HSC 25c
In a stack of 10 DVDs, there are 5 rated PG, 3 rated G and 2 rated M.
- A DVD is selected at random. What is the probability that it is rated M? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Grant chooses two DVDs at random from the stack. Copy or trace the tree diagram into your writing booklet.
- Complete the tree diagram by writing the correct probability on each branch. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- Calculate the probability that Grant chooses two DVDs with the same rating. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Show Answers Only
Show Worked Solution
i.
| ii. |  |
iii.
Probability, STD2 S2 2013 HSC 30b
In a class there are 15 girls (G) and 7 boys (B). Two students are chosen at random to be class representatives.
- Complete the tree diagram below. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- What is the probability that the two students chosen are of the same gender? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Show Answers Only
Show Worked Solution
i.
| ii. | ||
♦ Mean mark (ii) 40%.
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 ?
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.
- Complete the probability tree diagram below. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- Calculate the probability that the two scarves selected are made from silk. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Calculate the probability that the two scarves selected are made from different fabrics. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Show Answers Only
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
MARKER’S COMMENT: In better responses, students multiplied along the branches and then added these two results together