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A fair spinner has six sides - OCR - GCSE Maths - Question 1 - 2017 - Paper 1

Question 1

A fair spinner has six sides. They are labelled 1, 1, 2, 4, 4, 5. The diagram shows a probability scale. Which arrow shows the probability of (a) scoring a 2, (... show full transcript

Worked Solution & Example Answer:A fair spinner has six sides - OCR - GCSE Maths - Question 1 - 2017 - Paper 1

Step 1

(a) scoring a 2

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Answer

To determine the probability of scoring a 2, we first need to identify how many times the number 2 appears on the spinner. In this case, 2 appears once among the six sides of the spinner.

The probability can be calculated using the formula:

$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, we have:

$P(2) = \frac{1}{6}$

On the probability scale, this corresponds to arrow D, as it represents a value of approximately 0.167.

Step 2

(b) scoring a number less than 6

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Answer

The numbers on the spinner that are less than 6 are 1, 1, 2, 4, and 4. This amounts to 5 favorable outcomes.

Using the same formula for probability:

$P(<6) = \frac{5}{6}$

The probability scale will show this probability approaching 0.833.

Step 3

(c) scoring a 1 or a 4

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Answer

The number 1 appears twice and the number 4 appears twice as well. Therefore, the total favorable outcomes for scoring either a 1 or a 4 is 4.

This gives us:

$P(1 \text{ or } 4) = \frac{4}{6} = \frac{2}{3}$

This would be represented on the probability scale at about 0.667.

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