Higher June 2025 Paper 4 Q22
22 A school has 90 students in Year 11.
- 50 of the students study French.
- 59 of the students study Spanish.
- 4 of the students do not study either of these languages.
One the students is chosen at random.
Find the probability that the student studies French given that they study Spanish.
You may use the grid or the Venn diagram to help present your working if you wish. [5]
| Answer | Marks | Part marks and guidance | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\frac{23}{59}\) | 5 | If \(\frac{23}{59}\) in working isw conversion to another form and accept 0.3898… or 0.39[0] or 38.98% or 39[.0]% for 5 marks | |||||||||||||||
| B4 for answer \(\frac{23}{n}\) where \(24 \leqslant n \leqslant 90\) or B3 for (F and S) = 23 or M3 for a correct Venn diagram or correct table showing these figures in black or B2 for (S and not F) = 36 or for (F and not S) = 27 or for answer \(\frac{k}{59}\) where \(1 \leqslant k \leqslant 58\) or M2 for a Venn diagram or table with two of n(F)=50, n(S)=59 and n(\(\xi\))=90 correct or B1 for (not F) = 40 or (not S) = 31 or M1 for a Venn diagram or table with one of n(F)=50, n(S)=59 and n(\(\xi\))=90 correct | Award B marks if correctly shown on a labelled grid or implied on a Venn diagram
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