Calculate the probability that one of these two students studies French but not German and the other studies German but not French. You must show your working. [5]
Mark scheme (a)
Answer
Marks
Part marks and guidance
3
B2 for 8, 9 or 11 correctly placed or B1 for the total of F = 17 or for the total of G = 20 or for all 3 regions add up to 28 or for \(17 - x\), \(x\), \(20 - x\)
Do not accept a blank region to represent 0
Mark scheme (b)
Answer
Marks
Part marks and guidance
\(\dfrac{88}{435}\) oe or 0.202(…) with correct working
5
B1 for \(\dfrac{8}{30}\) oe soi or \(\dfrac{11}{30}\) soi M1 for P(F only, G only) [+] P(G only, F only) M1 for P(F only, G only) = their \(\dfrac{8}{30} \times\) their \(\dfrac{11}{29 \text{ or } 30}\) or their \(\dfrac{11}{30} \times\) their \(\dfrac{8}{29 \text{ or } 30}\) A1 for \(\dfrac{88}{870}\) or \(\dfrac{44}{435}\) or 0.101(…)
“Correct working” requires evidence of at least M1M1 eg correct branches identified on a tree or implied by their subsequent calculation FT their (a): their 8 and their 11 are FT their (a)
If 0, 1 or 2 scored, instead award SC3 for answer \(\dfrac{88}{435}\) oe or 0.202(…) with no or insufficient working If 0 or 1 scored SC2 for \(\dfrac{88}{870}\) or \(\dfrac{44}{435}\) or 0.101(…) with no or insufficient working If 0 scored SC1 for \(\dfrac{88}{450}\), \(\dfrac{44}{225}\) or 0.195[5..] to 0.196 with no working
Likely incorrect answers with working: B1M1M1 for answer \(\dfrac{88}{450}\), \(\dfrac{44}{225}\) or 0.195[5..] to 0.196 B1M0M1 for answer \(\dfrac{88}{900}\), \(\dfrac{44}{450}\), \(\dfrac{22}{225}\) or 0.097[7..] to 0.098
