C. 860. A survey carried out on a sample of 500 revealed that 46% of those asked liked strawberry ice cream, 71% liked vanilla and 85% liked chocolate ice cream. Is there anyone in the sample who likes all three flavours?

(5 points)

Deadline expired.

Sorry, the solution is published in Hungarian only.

Megoldás: Van.

A Venn-diagram alapján a következő egyenleteket írhatjuk föl:

a+b+c+d+e+f+g+h=500,

a+b+f+g=0,46^.500=230,

b+c+d+g=0,71^.500=355,

d+e+f+g=0,85^.500=425.

Ezek alapján

500-(230+355+425)=-510=(a+b+c+d+e+f+g+h)-(a+b+f+g)-(b+c+d+g)-(d+e+f+g)=h-(b+d+f+2g).

Vagyis (b+d+f+g)+g=500+(10+h), és mivel b+d+f+g legfeljebb 500, a jobboldal viszont legalább 510, ezért g legalább 10. Vagyis legalább 10 olyan ember van, aki mind a háromféle fagylaltot szereti.

Statistics on problem C. 860. 683 students sent a solution. 5 points: 577 students. 4 points: 13 students. 3 points: 25 students. 2 points: 15 students. 1 point: 9 students. 0 point: 34 students. Unfair, not evaluated: 10 solutions.