Higher June 2018 Paper 1 Q8
8 A coin is thrown 50 times.
It lands on heads 31 times.
(a) Write down the relative frequency it lands on heads. [1 mark]
(b) Raj says,
“The coin is biased towards heads.”
Use the data to give a reason why he might be correct. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{31}{50}\) or 0.62 or 62% | B1 | oe fraction, decimal or percentage |
Additional guidance
| 31 or 62 | B0 |
| 31 : 50 | B0 |
| 31 out of 50 or 31 in 50 | B0 |
| Ignore subsequent attempts to simplify \(\dfrac{31}{50}\) or convert it to a decimal or percentage, eg \(\dfrac{31}{50} = 0.6\) | B1 |
| \(\dfrac{31}{50} = 0.5\) oe is considered as choice | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Valid reason | B1ft | eg 31 is more than 19 (12) more heads than tails 31 is more than 25 \(31 \neq 25\) (6) more than expected it should be 25 times heads and tails should be (roughly) equal it landed on heads more than half the times relative frequency/probability is more than 0.5 ft if their \(0.62 \gt 0.5\) \(0.62 \gt 0.5\) ft if their \(0.62 \gt 0.5\) |
Additional guidance
| ft is only available if comparing their relative frequency to 0.5, and their relative frequency must be greater than 0.5 | |
| Condone the probability given as 50/50 in otherwise correct reasons eg Probability is 50/50 so there should be 25 heads | B1 |
| There were only 19 tails | B1 |
| There weren’t enough tails | B1 |
| Because it landed on heads 31 times and it should be 25/25 | B1 |
| It should be \(\dfrac{1}{2}\) | B1 |
| The probability should be \(\dfrac{1}{2}\) but it lands on heads 31 times | B1 |
| There were 31 heads | B0 |
| There were 19 tails | B0 |
| There were 31 heads and 19 tails | B0 |
| The coin could be fixed | B0 |
| Incorrect statement eg 31 is 22 more than 19 | B0 |