Question

Eight teams are competing in the quarter-finals of a world football championship title. Three out of them are European.

Answer 1

Answer: P(none of them Europeans play against each other)=$\frac{5}{14}$

Explanation:

Since there are 8 teams in which 3 are Europeans.

So, remaining 5 teams are not Europeans

We have to take 2 teams to pair up.

And we have a condition that neither of team is European.

So the favourable outcome =$\binom{5}{2}$

and the total outcomes=$\binom{8}{2}$

So, by using theprobability formula i.e.

P(E)=$\frac{\text{No. of favourable outcome}}{\text{Total no. of outcomes}}$

P(getting none of European team play against each other)=$\frac{\binom{5}{2}}{\binom{8}{3}}$

=$\frac{5\times4}{8\times7}$

=$\frac{5}{14}$