A fair six-sided die is repeatedly rolled. What is the minimum number of rolls required so that the probability of rolling a six at least once is greater than 0.95? (2 marks)
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Probability, 2ADV S1 2024 HSC 18
In a game, the probability that a particular player scores a goal at each attempt is 0.15.
- What is the probability that this player does NOT score a goal in the first two attempts? (1 mark)
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- Determine the least number of attempts that this player must make so that the probability of scoring at least one goal is greater than 0.8. (2 marks)
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Probability, 2ADV S1 2023 MET2 8 MC
A box contains
In 8 such selections, where
Probability, 2ADV S1 2022 HSC 15
In a bag there are 3 six-sided dice. Two of the dice have faces marked 1, 2, 3, 4, 5, 6. The other is a special die with faces marked 1, 2, 3, 5, 5, 5.
One die is randomly selected and tossed.
- What is the probability that the die shows a 5? (1 mark)
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- Given that the die shows a 5, what is the probability that it is the special die? (1 mark)
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Probability, 2ADV S1 2022 HSC 9 MC
Liam is playing two games. He is equally likely to win each game. The probability that Liam will win at least one of the games is 80%.
Which of the following is closest to the probability that Liam will win both games?
- 31%
- 40%
- 55%
- 64%
Probability, 2ADV S1 2019 MET2-N 9 MC
At the start of a particular week, Kim has three red apples and two green apples. She eats one apple everyday. On Monday, Tuesday and Wednesday of that week, she randomly selects an apple to eat. In this three-day period, the probability that Kim does not eat an apple of the same colour on any two consecutive days is
Probability, 2ADV S1 2019 HSC 6 MC
A game is played by tossing an ordinary 6-sided die and an ordinary coin at the same time. The game is won if the uppermost face of the die shows an even number or the uppermost face of the coin shows a tail (or both).
What is the probability of winning this game?
Probability, 2ADV S1 2018 HSC 14e
Two machines,
- One pen is chosen at random from each machine.
What is the probability that at least one of the pens is faulty? (1 mark)
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- A coin is tossed to select one of the two machines. Two pens are chosen at random from the selected machine.
What is the probability that neither pen is faulty? (2 marks)
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Probability, 2ADV S1 2018 HSC 6 MC
A runner has four different pairs of shoes.
If two shoes are selected at random, what is the probability that they will be a matching pair?
Probability, 2ADV S1 2016 HSC 15b
An eight- sided die is marked with numbers 1, 2, … , 8. A game is played by rolling the die until an 8 appears on the uppermost face. At this point the game ends.
- Using a tree diagram, or otherwise, explain why the probability of the game ending before the fourth roll is
. (2 marks)
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- What is the smallest value of
for which the probability of the game ending before the th roll is more than ? (3 marks)
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Probability, 2ADV S1 2007 HSC 9b
A pack of 52 cards consists of four suits with 13 cards in each suit.
- One card is drawn from the pack and kept on the table. A second card is drawn and placed beside it on the table. What is the probability that the second card is from a different suit to the first? (1 mark)
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- The two cards are replaced and the pack shuffled. Four cards are chosen from the pack and placed side by side on the table. What is the probability that these four cards are all from different suits? (2 marks)
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Probability, 2ADV S1 2006 HSC 4c
A chessboard has 32 black squares and 32 white squares. Tanya chooses three different squares at random.
- What is the probability that Tanya chooses three white squares? (2 marks)
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- What is the probability that the three squares Tanya chooses are the same colour?. (1 mark)
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- What is the probability that the three squares Tanya chooses are not the same colour? (1 mark)
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Probability, 2ADV S1 2005 HSC 5d
A total of 300 tickets are sold in a raffle which has three prizes. There are 100 red, 100 green and 100 blue tickets.
At the drawing of the raffle, winning tickets are NOT replaced before the next draw.
- What is the probability that each of the three winning tickets is red? (2 marks)
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- What is the probability that at least one of the winning tickets is not red? (1 mark)
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- What is the probability that there is one winning ticket of each colour? (2 marks)
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Probability, 2ADV S1 2004 HSC 1e
A packet contains 12 red, 8 green, 7 yellow and 3 black jellybeans.
One jellybean is selected from the packet at random.
What is the probability that the selected jellybean is red or yellow? (2 marks)
Probability, 2ADV S1 2008 HSC 9a
It is estimated that 85% of students in Australia own a mobile phone.
- Two students are selected at random. What is the probability that neither of them owns a mobile phone? (2 marks)
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- Based on a recent survey, 20% of the students who own a mobile phone have used their mobile phone during class time. A student is selected at random. What is the probability that the student owns a mobile phone and has used it during class time? (1 mark)
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Probability, 2ADV S1 2009 HSC 5b
On each working day James parks his car in a parking station which has three levels. He parks his car on a randomly chosen level. He always forgets where he has parked, so when he leaves work he chooses a level at random and searches for his car. If his car is not on that level, he chooses a different level and continues in this way until he finds his car.
- What is the probability that his car is on the first level he searches? (1 mark)
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- What is the probability that he must search all three levels before he finds his car? (1 mark)
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- What is the probability that on every one of the five working days in a week, his car is not on the first level he searches? (1 mark)
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Probability, 2ADV S1 2010 HSC 4c
There are twelve chocolates in a box. Four of the chocolates have mint centres, four have caramel centres and four have strawberry centres. Ali randomly selects two chocolates and eats them.
- What is the probability that the two chocolates have mint centres? (1 mark)
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- What is the probability that the two chocolates have the same centre? (1 mark)
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- What is the probability that the two chocolates have different centres? (1 mark)
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Probability, 2ADV S1 2012 HSC 13c
Two buckets each contain red marbles and white marbles. Bucket
Chris randomly chooses one marble from each bucket.
- What is the probability that both marbles are red? (1 mark)
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- What is the probability that at least one of the marbles is white? (1 mark)
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- What is the probability that both marbles are the same colour? (2 marks)
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Probability, 2ADV S1 2013 HSC 15d
Pat and Chandra are playing a game. They take turns throwing two dice. The game is won by the first player to throw a double six. Pat starts the game.
- Find the probability that Pat wins the game on the first throw. (1 mark)
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- What is the probability that Pat wins the game on the first or on the second throw? (2 marks)
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- Find the probability that Pat eventually wins the game. (2 marks)
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