Bayes Theorem This summer 32 national teams will participate

Bayes Theorem

This summer, 32 national teams will participate to the FIFA world cup 2014 in Brazil. At the tournament, 13 of the 32 teams are from Europe. Each national team has 23 football players. Each player also belongs to a football club (for example Juventus, Manchester United or Boca Juniors), which is located in either Europe or the Rest of the World. We know the following facts about players participating to the world cup: among those players who play for a european club, the probability they play for a european nation is 350/736; among those players who do not play for a european club, the probability they play for a european nation is 1/736. What is the probability that a player at the world cup plays for a european club? There is not enough information for computing it 298 349

Solution

probability that aplayer at the world cup plays for a european club is

13/32 * 350 / 736    +    13/32 * 1 / 736

0.1932 + 0.00055197

0.193752