Higher June 2023 Paper 3 Q12
12 Here is a biased spinner.
(a) Ali, Ben and Cary want to know the probability of spinning red on the biased spinner.
They each spin it and count how many times it lands on red and divide by the total number of spins.
| Ali says | “I spun red the most times” |
| Ben says | “I spun the spinner the most times” |
| Cary says | “My relative frequency of red is 0.25” |
Who had the best estimate for the probability of spinning red?
Give a reason for your answer. [1 mark]
(b) Dev spins the spinner 80 times.
He says,
“My relative frequency of red is 0.185”
Give a reason why his relative frequency must be wrong. [1 mark]
(c) Elena spins the spinner 125 times.
The relative frequency of red is 0.32
Work out how many times the spinner landed on green. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Ben and valid reason | B1 | eg spun the most times |
Additional guidance
Do not accept an incorrect reason alongside a correct response
Do not accept reasons which refer to the probability increasing
Ignore reasons that refer to results being more accurate
| Answer | Mark | Comments |
|---|---|---|
| Valid reason | B1 | eg 14.8 is not a whole number |
Additional guidance
| Do not accept an incorrect reason alongside a correct response | |
| \(0.185 \times 80\) is not a whole number | B1 |
| Number of spins would be a decimal | B1 |
| Number of spins must be a whole number | B1 |
| Cannot land on the spinner 14.8 times | B1 |
| Have to spin 14.8 times | B0 |
| \(0.185 \times 80 = 14.8\) | B0 |
| 14.8 | B0 |
| It is a decimal | B0 |
| Must be a whole number | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(125 \times 0.32\) or 40 or \(1 - 0.32\) or 0.68 | M1 | oe |
| 85 | A1 |