Question

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

If the teams are paired randomly, what is the probability that none of the European teams have to play against each
other?

Answer 1

Answer: P(none of them Europeans play against each other)=
`(5)/(14)`

Step-by-step 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}}`

=
`(5*4)/(8*7)`

=
`(5)/(14)`