One hundred tickets are sold in a raffle which offers two prizes. Hazel buys five of the tickets. A ticket is drawn at random for the first prize. A second ticket is drawn from the remaining tickets for the other prize. What is the probability that Hazel wins both prizes? (2 marks)
Probability, STD2 S2 2020 HSC 15 MC
The top of a rectangular table is divided into 8 equal sections as shown.
A standard die with faces labelled 1 to 6 is rolled onto the table. The die is equally likely to land in any of the 8 sections of the table. If the die does not land entirely in one section of the table, it is rolled again.
A score is calculated by multiplying the value shown on the top face of the die by the number shown in the section of the table where the die lands.
What is the probability of getting a score of 6?
- `frac{1}{48}`
- `frac{1}{12}`
- `frac{1}{8}`
- `frac{1}{6}`
Show Worked Solution
`text{Strategy 1}`
♦ Mean mark 40%.
`text{Combinations that score 6:}`
`4 \ text{combinations score} \ 6`
| `therefore \ P(6)` | `= 4 xx frac{1}{8} xx frac{1}{6}` |
| `= frac{1}{12}` |
`text{Strategy 2}`
| `Ptext{(6)}` | `= Ptext{(T1)}Ptext{(D6)} + Ptext{(T2)}Ptext{(D3)} + Ptext{(T3)}Ptext{(D2)} + Ptext{(T6)}Ptext{(D1)}` |
| `= frac{1}{8} xx frac{1}{6} + frac{1}{8} xx frac{1}{6} + frac{1}{8} xx frac{1}{6} + frac{1}{8} xx frac{1}{6}` | |
| `= 4 xx frac{1}{8} xx frac{1}{6}` | |
| `= frac{1}{12}` |
`=> \ B`
Probability, STD2 S2 2011 HSC 26a
The two spinners shown are used in a game.
Each arrow is spun once. The score is the total of the two numbers shown by the arrows.
A table is drawn up to show all scores that can be obtained in this game.
- What is the value of `X` in the table? (1 mark)
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- What is the probability of obtaining a score less than 4? (1 mark)
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- On Spinner `B`, a 2 is obtained. What is the probability of obtaining a score of 3? (1 mark)
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Probability, STD2 S2 2017 HSC 24 MC
A deck of 52 playing cards contains 12 picture cards. Two cards from the deck are drawn at random and placed on a table.
What is the probability, correct to four decimal places, that exactly one picture card is on the table?
A. `0.0498`
B. `0.1810`
C. `0.3550`
D. `0.3620`
Probability, STD2 S2 2015 HSC 16 MC
The probability of winning a game is `7/10`.
Which expression represents the probability of winning two consecutive games?
- `7/10 xx 6/9`
- `7/10 xx 6/10`
- `7/10 xx 7/9`
- `7/10 xx 7/10`
Probability, STD2 S2 2006 HSC 25c
Sonia buys three raffle tickets.
- What is the probability that Sonia wins first prize? (1 mark)
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- What is the probability that she wins both prizes? (2 marks)
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Probability, STD2 S2 2006 HSC 10 MC
Kay randomly selected a marble from a bag of marbles, recorded its colour and returned it to the bag. She repeated this process a number of times.
Based on these results, what is the best estimate of the probability that Kay will choose a green marble on her next selection?
- `5/24`
- `1/24`
- `1/6`
- `1/5`
Probability, STD2 S2 2004 HSC 18 MC
Two dice are rolled. What is the probability that only one of the dice shows a six?
- `5/36`
- `1/6`
- `5/18`
- `11/36`
Probability, STD2 S2 2007 HSC 10 MC
Each time she throws a dart, the probability that Mary hits the dartboard is `2/7`.
She throws two darts, one after the other.
What is the probability that she hits the dartboard with both darts?
- `1/21`
- `4/49`
- `2/7`
- `4/7`
Probability, STD2 S2 2008 HSC 22 MC
A die has faces numbered 1 to 6. The die is biased so that the number 6 will appear more often than each of the other numbers. The numbers 1 to 5 are equally likely to occur.
The die was rolled 1200 times and it was noted that the 6 appeared 450 times.
Which statement is correct?
- The probability of rolling the number 5 is expected to be `1/7`.
- The number 6 is expected to appear 2 times as often as any other number.
- The number 6 is expected to appear 3 times as often as any other number.
- The probability of rolling an even number is expected to be equal to the probability of rolling an odd number.
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?
- `8/31 xx 7/30`
- `8/31 xx 7/31`
- `8/31 xx 8/30`
- `8/31 xx 8/31`
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)
Probability, STD2 S2 2013 HSC 26c
The probability that Michael will score more than 100 points in a game of bowling is `31/40`.
- A commentator states that the probability that Michael will score less than 100 points in a game of bowling is `9/40`.
Is the commentator correct? Give a reason for your answer. (1 mark)
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- 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)
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Probability, STD2 S2 2012 HSC 12 MC
Two unbiased dice, each with faces numbered 1, 2, 3, 4, 5, 6, are rolled.
What is the probability of a 6 appearing on at least one of the dice?
- `1/6`
- `11/36`
- `25/36`
- `5/6`
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?
- `1/6`
- `1/12`
- `5/12`
- `5/36`