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-004 MC
Peter has a bag of marbles. 75% of his marbles are blue.
Peter takes a green marble from his bag and loses it in a game.
If he takes another marble from the bag without looking, what are the chances it is blue?
- less than 75%
- equal to 75%
- greater than 75%
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 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