smc-829-50-Arrays

Probability, STD2 S2 2023 HSC 8 MC

A game involves throwing a die and spinning a spinner.

The sum of the two numbers obtained is the score.

The table of scores below is partially completed.

What is the probability of getting a score of 7 or more?

`1/6`
`1/4`
`5/18`
`5/12`

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`D`

Show Worked Solution

`Ptext{(score 7+)} = 10/24=5/12`

`=>D`

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}`

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`B`

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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`5`
`1/2`
`2/3`

Show Worked Solution

i. `X=3+2=5`

ii. `P(text{score}<4)=6/12=1/2`

iii. `P(3)=2/3`

Probability, STD2 S2 2009 HSC 28d

In an experiment, two unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6 are rolled 18 times.

The difference between the numbers on their uppermost faces is recorded each time. Juan performs this experiment twice and his results are shown in the tables.

Juan states that Experiment 2 has given results that are closer to what he expected than the results given by Experiment 1.

Is he correct? Explain your answer by finding the sample space for the dice differences and using theoretical probability. (4 marks)

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`text{Juan is correct (See Worked Solutions)}`

Show Worked Solution

♦♦♦ Mean mark 7%. Toughest question in the 2009 exam.
MARKER’S COMMENT: This question guides students by asking for an explanation using the sample space for the dice differences. This step alone received 2 full marks. Note that instructions to explain your answer requires mathematical calculations to support an argument.

`text(Sample space for dice differences)`

`text(Juan is correct. The table shows Experiment 1)`

`text(has greater total differences to the expected)`

`text(frequencies than Experiment 2)`