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This is a fair 5-sided spinner - OCR - GCSE Maths - Question 21 - 2017 - Paper 1
Question 21
This is a fair 5-sided spinner. Ciara spins the spinner twice and records the product of the two scores. (i) Complete the table. First spin x 1 2 3 4 ... show full transcript
Worked Solution & Example Answer:This is a fair 5-sided spinner - OCR - GCSE Maths - Question 21 - 2017 - Paper 1
Step 1
(i) Complete the table
Answer
To complete the table, we calculate the product for each combination of scores from the two spins. The completed table will look like this:
First spin
x 1 2 3 4 5
Second spin
1 | 1 | 2 | 3 | 4 | 5 |
2 | 2 | 4 | 6 | 8 | 10 |
3 | 3 | 6 | 9 | 12 | 15 |
4 | 4 | 8 | 12 | 16 | 20 |
5 | 5 | 10 | 15 | 20 | 25 |
Each cell is filled with the product of the first and second spin scores.
Step 2
(ii) Find the probability that the product is a multiple of 3
Answer
To find the probability that the product is a multiple of 3, we need to count the outcomes in the completed table.
The products that are multiples of 3 are 3, 6, 9, 12, and 15. Counting these:
- From the table, we see:
- 3 (1x3)
- 6 (2x3, 3x2)
- 9 (3x3)
- 12 (3x4, 4x3)
- 15 (3x5, 5x3)
Next, we calculate the total number of successful outcomes.
Overall, there are 5 numbers on the spinner, giving us a total of 5 * 5 = 25 outcomes when spun twice.
The probability of the product being a multiple of 3 is thus: rac{9}{25}