Foundation November 2024 Paper 3 Q11
11 In a particular town last year:
- it rained on 17 of the 30 days in November
- it rained on 18 of the 31 days in December.
(a) Which month, November or December, had the highest proportion of rainy days?
Show how you decide.
Show how you decide.
............................... because ............................... [3]
(b) Sam says,
I think the probability it will rain on December 25th next year is \(\dfrac{18}{31}\).
What assumption has Sam made? [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| December and two correct values in comparable form | 3 | Allow B and M marks, even if not used in final reason or November chosen B2 for 0.56 to 0.57 and 0.58[0] to 0.58[1] or 56% to 57% and 58[.0]% to 58[.1]% or \(\dfrac{17 \times 31}{30 \times 31}\) and \(\dfrac{18 \times 30}{30 \times 31}\) or better or M1 for \(\dfrac{17}{30}\) or \(17 \div 30\) soi by 0.56 to 0.57 or \(\dfrac{18}{31}\) or \(18 \div 31\) soi by 0.58[0] to 0.58[1] | Values may be in working isw attempts to change form once correct value seen Condone \(0.\dot{5}8\) for 0.58 Condone any missing % signs Accept 527 and 540 for \(\dfrac{17 \times 31}{30 \times 31}\) and \(\dfrac{18 \times 30}{30 \times 31}\) Alternatively accept for all marks \(\dfrac{13}{30}\) and \(\dfrac{13}{31}\) soi by 0.43[3] or \(0.4\dot{3}\) and 0.41 to 0.42 etc or \(\dfrac{30}{17}\) and \(\dfrac{31}{18}\) soi by 1.76 or \(1.\dot{7}6\) and 1.72 or \(1.7\dot{2}\) etc May also be \(\dfrac{30}{13}\) and \(\dfrac{31}{13}\) oe and division e.g. \(30 \div 13\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Relative frequency can be used as an estimate of probability Probability/proportion of rainy days is the same as last year | 1 | See appendix Do not accept amount / number of times / rain / weather for “number of rainy days” | |
Appendix
Question 11(b)
| Response | Mark | |
|---|---|---|
| There will be the same proportion of rainy days as the year before | Reason correct | 1 |
| It will be the same number of rainy days in December every year | BOD including “every” in the statement | 1 |
| There will be 18 rainy days in December next year | Reason correct | 1 |
| It will not rain on 13 days next year | Reason correct | 1 |
| It will rain 18/31 days in December | BOD 18/31 as 18 “out of” 31 | 1 |
| December next year will have the same (amount of) rainfall as last December | Does not mention “number of days” | 0 |
| Each day will have the same chance of rain | Not a proportion and doesn’t reference last year | 0 |
| That the highest proportion will remain the same | No mention of proportion of rainy days | 0 |
| Rainy days occur at random/independently | Doesn’t justify the given probability | 0 |
| Rainy days are equally distributed | Doesn’t justify the given probability | 0 |
| That it rains the same amount of times each year in every December | Does not mention “number of days” | 0 |
| That rainfall will stay the same | Does not mention “number of days” | 0 |
| He has assumed that it will be the same every year | Does not mention “number of days” | 0 |
| It will rain on the same days next year | Does not say NUMBER of days | 0 |