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Geoff has two fair spinners - OCR - GCSE Maths - Question 16 - 2018 - Paper 2
Question 16
Geoff has two fair spinners. He spins both spinners and multiplies the numbers on each spinner. (a) Complete the table. Spinner A Spinner B \( x \) | 1 | 7 ... show full transcript
Worked Solution & Example Answer:Geoff has two fair spinners - OCR - GCSE Maths - Question 16 - 2018 - Paper 2
Step 1
Complete the table:
Answer
To complete the table, we multiply the values from Spinner A by those from Spinner B:
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For ( x = 2 ):
- ( 2 \times 1 = 2 )
- ( 2 \times 7 = 14 )
- ( 2 \times 9 = 18 )
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For ( x = 3 ):
- ( 3 \times 1 = 3 )
- ( 3 \times 7 = 21 )
- ( 3 \times 9 = 27 )
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For ( x = 4 ):
- ( 4 \times 1 = 4 )
- ( 4 \times 7 = 28 )
- ( 4 \times 9 = 36 )
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For ( x = 5 ):
- ( 5 \times 1 = 5 )
- ( 5 \times 7 = 35 )
- ( 5 \times 9 = 45 )
Thus the completed table should reflect these calculations.
Step 2
Explain his error and give the correct answer.
Answer
Geoff's approach to find the probability includes considering even and prime numbers solely by subtracting probabilities, which is incorrect because these two categories are not mutually exclusive.
- The number 2 is both an even number and a prime number. Thus, when calculating the probability of being an even number or a prime number, the overlap should not be double counted.
To calculate the correct probability:
- The probability of an even number is: ( \frac{6}{12} )
- The probability of a prime number is: ( \frac{3}{12} )
- The probability of both occurring (the number 2 being counted in both categories) is: ( \frac{1}{12} )
The correct formula is:
[ P(Even \cup Prime) = P(Even) + P(Prime) - P(Even \cap Prime) = \frac{6}{12} + \frac{3}{12} - \frac{1}{12} = \frac{8}{12} = \frac{2}{3} ]
Thus, the correct probability of obtaining an even number or a prime number is ( \frac{2}{3} ).