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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
Complete the table.
Answer
To fill out the table, we calculate the product of the scores from the two spins:
-
For the first spin of 1:
- 1 × 1 = 1
- 1 × 2 = 2
- 1 × 3 = 3
- 1 × 4 = 4
-
For the first spin of 2:
- 2 × 1 = 2
- 2 × 2 = 4
- 2 × 3 = 6
- 2 × 4 = 8
-
For the first spin of 3:
- 3 × 1 = 3
- 3 × 2 = 6
- 3 × 3 = 9
- 3 × 4 = 12
-
For the first spin of 4:
- 4 × 1 = 4
- 4 × 2 = 8
- 4 × 3 = 12
- 4 × 4 = 16
Thus, the completed table is:
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 |
| 2 | 2 | 4 | 6 | 8 |
| 3 | 3 | 6 | 9 | 12 |
| 4 | 4 | 8 | 12 | 16 |
Step 2
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 first identify all the possible outcomes when spinning the spinner twice. There are a total of 5 options for each spin, resulting in:
Total outcomes = 5 × 5 = 25
Next, we look for products that are multiples of 3:
- From the table, the products that are multiples of 3 are:
- 3 (from 1 × 3)
- 6 (from 2 × 3 or 3 × 2)
- 9 (from 3 × 3)
- 12 (from 3 × 4 or 4 × 3)
- 12 (from 4 × 3)
Counting these outcomes:
- Products that are multiples of 3: 3, 6, 6, 9, 12, 12 → Total = 6 outcomes
So, the probability that the product is a multiple of 3 is:
Probability = ( rac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{25} )