A game involves throwing a die and spinning a spinner - HSC - SSCE Mathematics Advanced - Question 2 - 2023 - Paper 1
Question 2
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 ... show full transcript
Worked Solution & Example Answer:A game involves throwing a die and spinning a spinner - HSC - SSCE Mathematics Advanced - Question 2 - 2023 - Paper 1
Step 1
Determine possible scores
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Answer
To calculate the possible scores of 7 or more, let's first identify the score combinations based on the scores from the die and the spinner.
The maximum score occurs when both the die and spinner land on 6 and 4 respectively, totaling to:
Die: 5 + Spinner: 4 = 9
Die: 4 + Spinner: 3 = 7
Next, let's list all the combinations that yield scores of 7 or more:
(3, 4) → Score: 7
(4, 3) → Score: 7
(5, 2) → Score: 7
(6, 1) → Score: 7
(5, 3) → Score: 8
(4, 4) → Score: 8
(3, 5) → Score: 8
(5, 4) → Score: 9
(6, 2) → Score: 8
(6, 3) → Score: 9
(6, 4) → Score: 10
This totals 10 combinations.
Step 2
Calculate total outcomes
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Answer
The die has 6 faces, and the spinner has 4 sections, yielding total outcomes as follows:
6imes4=24
This means there are 24 possible outcomes in total.
Step 3
Determine the probability
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Answer
To find the probability of scoring 7 or more, we can use the formula for probability:
P(A)=Total outcomesNumber of favorable outcomes=2410=125
Thus, the probability of getting a score of 7 or more is ( \frac{5}{12} ).
