This is a fair 5-sided spinner. Ciara spins the spinner twice and records the product of the two scores. (i) Complete the table. | x | 1 | 2 | 3 | 4 | |---|---|---|---|---| | 1 | | | | | | 2 | | | | | | 3 | | | | | | 4 | | | | | (ii) Find the probability that the product is a multiple of 3. (b) Ciara makes a different fair 5-sided spinner. She spins the spinner twice and records the product of the two scores. Ciara says The probability that the product is negative is 0.48. Write numbers on the spinner below so that Ciara's statement is correct.

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This is a fair 5-sided spinner - OCR - GCSE Maths - Question 6 - 2017 - Paper 1

Question 6

This is a fair 5-sided spinner. Ciara spins the spinner twice and records the product of the two scores. (i) Complete the table. | x | 1 | 2 | 3 | 4 | |---|---|--... show full transcript

Worked Solution & Example Answer:This is a fair 5-sided spinner - OCR - GCSE Maths - Question 6 - 2017 - Paper 1

Step 1

Complete the table.

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Answer

To complete the table, we multiply the scores from the first spin with the scores from the second spin. The products are as follows:

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

Here, each cell represents the product of the corresponding row and column headers.

Step 2

Find the probability that the product is a multiple of 3.

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Answer

To find the probability that the product is a multiple of 3, we first analyze the products:

The products that are multiples of 3 from our table are:

3 (1,3)
6 (2,3 and 3,2)
9 (3,3)
12 (3,4 and 4,3)

Counting the favorable outcomes, we find a total of 6 outcomes that are multiples of 3. The total number of possible outcomes is 25 (5 scores for the first spin multiplied by 5 for the second spin).

Thus, the probability is given by: $P(multiple ext{ }of ext{ }3) = \frac{6}{25}$

Step 3

Write numbers on the spinner below so that Ciara's statement is correct.

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Answer

To satisfy Ciara's statement (the probability that the product is negative is 0.48), we can use a certain configuration of numbers on the spinner. For example:

1, 1, -1, -1, -1

With these numbers, we have 2 positive and 3 negative outcomes. The product of two spins will be negative if one of the scores is positive and the other negative.

Calculating the probability:

Total outcomes = 25 (5x5)
Favorable outcomes (1 positive with 1 negative): 2 (positives) * 3 (negatives) = 6.
Therefore, the probability that the product is negative is: $P(negative) = \frac{6}{25} = 0.48$

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Questions answered

This is a fair 5-sided spinner - OCR - GCSE Maths - Question 6 - 2017 - Paper 1

Worked Solution & Example Answer:This is a fair 5-sided spinner - OCR - GCSE Maths - Question 6 - 2017 - Paper 1

Complete the table.

Find the probability that the product is a multiple of 3.

Write numbers on the spinner below so that Ciara's statement is correct.

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