Foundation November 2023 Paper 3 Q13
13 There are 1400 students at a college.
A student is chosen at random.
(a) The probability that the student is taking a GCSE resit is 0.09
How many of the students are taking a GCSE resit? [2 marks]
(b) The probability that the student is studying
A-levels is 0.67
Core Maths is 0.48
Show that some students are studying A-levels and Core Maths. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.09 \times 1400\) | M1 | oe |
| 126 | A1 |
Additional guidance
| M1 may be awarded for correct work, with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Do not ignore further working after 126 seen | |
| Do not allow a misread of 0.9 for 0.09 | |
| \(1400 - 126 = 1274\) in working | M1 |
| \(\dfrac{126}{1400}\) in working | M1 |
| \(\dfrac{126}{1400}\) on answer line | M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(0.67 + 0.48 = 1.15\) and the sum (of the probabilities) is greater than 1 or \(0.67 + 0.48 = 1.15\) and 0.15 study both or \(0.67 + 0.48 = 1.15\) and more than the total number of students at school | B2 | oe B1 1.15 oe or the sum (of the probabilities) is greater than 1 or 0.15 oe |
| Alternative method 2 | ||
| \(938 + 672 = 1610\) and more than the total number of students at school or \(938 + 672 = 1610\) and the total (number of students) is greater than 1400 or 938 and 672 and 210 study both | B2 | oe B1 \(0.67 \times 1400\) oe and \(0.48 \times 1400\) oe or 938 and 672 or 1610 or the total (number of students) is greater than 1400 or 210 |
Additional guidance
| B1 may be awarded for correct work, with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| \(938 + 672 = 1610\) and \(1610 \gt 1400\) | B2 |
| \(938 + 672 = 1610\) and students doing both as more than the total | B2 |
| \(0.67 + 0.48 = 1.15\) and \(1.15 \gt 1\) | B2 |
| \(67 + 48 = 115\) and students doing both as over 100 | B2 |
| \(67 + 48 = 115\) and 15% doing both | B2 |
| \(67 + 48 = 115\) and 15 doing both | B1 |
| \(0.67 + 0.48 = 1.15\) and needs to add to one | B1 |
| \(67 + 48 = 115\) | B1 |
| \(0.67 + 0.48 = 1.15\) and students doing both as over 100 (must be consistent form for comparison) | B1 |
| \(\dfrac{938}{1400}\) and \(\dfrac{672}{1400}\) | B1 |
| \(0.67 + 0.48\) is more than 1 | B1 |