Higher June 2018 Paper 3 Q20

EdexcelCurrent spec5 marksMultiple Events Sets

20 50 people were asked if they speak French or German or Spanish.

Of these people,

31 speak French
2 speak French, German and Spanish
4 speak French and Spanish but not German
7 speak German and Spanish
8 do not speak any of the languages
all 10 people who speak German speak at least one other language

Two of the 50 people are chosen at random.

Work out the probability that they both only speak Spanish. (5)

Venn diagram for French, German and Spanish: French only 22, French and German only 3, German only 0, all three 2, French and Spanish only 4, German and Spanish only 5, Spanish only 6, none 8 — Mark scheme

Answer	Mark	Mark scheme
\(\dfrac{6}{490}\)	P1	for start to process information, eg draws Venn diagram and shows at least 1 unknown amount, eg 5 speak German and Spanish but not French
	P1	for process to find at least 3 unknown amounts from, eg 5 speak German and Spanish but not French 3 speak French and German but not Spanish 22 speak French but not German or Spanish 0 speak German but not French or Spanish
	P1	for complete process to find number of people who speak only Spanish (= 6)
	P1	for \(\dfrac{[\text{number speaking Spanish only}]}{50} \times \dfrac{[\text{number speaking Spanish only}] - 1}{49}\), eg \(\dfrac{6}{50} \times \dfrac{5}{49}\)
	A1	for \(\dfrac{6}{490}\) oe

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