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Geoff has two fair spinners - OCR - GCSE Maths - Question 3 - 2018 - Paper 5
Question 3
Geoff has two fair spinners. He spins both spinners and multiplies the numbers on each spinner. (a) Complete the table. Spinner A Spinner B 2 3 4 5 1 7 ... show full transcript
Worked Solution & Example Answer:Geoff has two fair spinners - OCR - GCSE Maths - Question 3 - 2018 - Paper 5
Step 1
Complete the table.
Answer
To complete the table for the multiplication of the numbers from Spinner A and Spinner B, we find the products as follows:
-
For Spinner B = 2:
- 1 x 2 = 2
- 7 x 2 = 14
- 9 x 2 = 18
-
For Spinner B = 3:
- 1 x 3 = 3
- 7 x 3 = 21
- 9 x 3 = 27
-
For Spinner B = 4:
- 1 x 4 = 4
- 7 x 4 = 28
- 9 x 4 = 36
-
For Spinner B = 5:
- 1 x 5 = 5
- 7 x 5 = 35
- 9 x 5 = 45
The completed table:
| Spinner B \ Spinner A | 1 | 7 | 9 |
|---|---|---|---|
| 2 | 2 | 14 | 18 |
| 3 | 3 | 21 | 27 |
| 4 | 4 | 28 | 36 |
| 5 | 5 | 35 | 45 |
Step 2
Explain his error and give the correct answer.
Answer
Geoff's reasoning is incorrect because he counts the outcomes of being even and prime without considering that some numbers belong to both categories, hence counting them twice.
For a correct calculation:
- The total number of outcomes from multiplying both spinners is 12 (3 outcomes from Spinner B times 4 outcomes from Spinner A).
- The even outcomes are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (total of 8 outcomes).
- The prime outcomes from multiplication include numbers like: 3, 5, 7, 11, etc. (Here, we need to check by actual products).
After recalculating, the corrected probability of getting either an even or prime number when multiplying the numbers is:
Total Outcomes for even and prime:
- For even: 8 outcomes (2, 4, 6, 8, 10, 12, 14, 16, 18, 20)
- For prime: 3 outcomes (3, 5, and 7 from our checking)
Combining these outcomes and correcting for shared outcomes as necessary gives:
Thus, the corrected answer is rac{5}{6}.