What is the probability of getting a score of 7 or more?
A - HSC - SSCE Mathematics Standard - Question 11 - 2023 - Paper 1
Question 11
What is the probability of getting a score of 7 or more?
A. 1
Worked Solution & Example Answer:What is the probability of getting a score of 7 or more?
A - HSC - SSCE Mathematics Standard - Question 11 - 2023 - Paper 1
Step 1
Identify Scores of 7 or More
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Answer
From the provided spinner and die combinations, we can identify which combinations yield a score of 7 or more. The combinations from the spinner (1-4) and die (1-6) are totaled as follows:
Die rolls 1: Scores = 2, 3, 4 (total: 1)
Die rolls 2: Scores = 3, 4, 5 (total: 3)
Die rolls 3: Scores = 4, 5, 6 (total: 3)
Die rolls 4: Scores = 5, 6, 7 (total: 3)
Die rolls 5: Scores = 6, 7, 8 (total: 3)
Die rolls 6: Scores = 7, 8, 9 (total: 3)
The valid combinations that yield a score of 7 or more are:
(3,4) -> 7
(4,3) -> 7
(5,2) -> 7
(6,1) -> 7
(6,2) -> 8
(6,3) -> 9
(5,3) -> 8
(5,4) -> 9
Thus, the successful outcomes for a score of 7 or more are 7 in total.
Step 2
Determine Total Possible Outcomes
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Answer
The total outcomes can be determined by multiplying the number of choices on the spinner (4 options) by the number of choices on the die (6 options).
Total outcomes = 4 (spinner) * 6 (die) = 24.
Step 3
Calculate Probability
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Answer
The probability of getting a score of 7 or more is calculated by dividing the number of successful outcomes by the total number of possible outcomes:
P(7ormore)=Total outcomesNumber of successful outcomes=247
Thus, the probability of getting a score of 7 or more is ( \frac{7}{24} ).
