The probability of a team in World Cup Belgium, Croatia, England and France have
ID: 3071444 • Letter: T
Question
The probability of a team in World Cup
Belgium, Croatia, England and France have reached the semifinal of the World Cup. The betting agency ProFoot has announced their estimated probabilities for the games between these four teams in the following table Belgium t England France Belgium Croatia 0.6 0.6 0.5 0.4 0.4 0.3 0.1 0.5 0.7 France0.6 0.9 For instance, the entry 0.9 indicates that the ProFoot believes that the probability that (a) Suppose that the semifinals are played by Belgium vs. England and Croatia vs. France (b) Suppose that the semifinals are played by Belgium vs. Croatia and England vs. France France defeats Croatia is 90 percent. What is the probability (according to ProFoot) that France wins the cup? What is the probability that France wins the world cup? (c) Suppose that the semifinal games are determined randomly. In other words, assume that the opponent of Belgium is randomly chosen from remaining three teams, each with probability 1/3, and the other two teams face each other. What is the probability that Belgium makes it to the final?Explanation / Answer
a)P(France wins the cup)=
P(France wins from Croatia and Belgium wins England and France wins Belgium)+P(France wins from Croatia and England wins Belgium and France wins England )
=0.7*0.6*0.6+0.7*0.4*0.9=0.504
b)
P(France wins from England and Belgium wins Croatia and France wins Belgium)+P(France wins from England and Croatia wins Belgium and France wins Croatia )
=0.9*0.4*0.6+0.9*0.6*0.7=0.594
c)
P(Belgium reaches final)=P(semi with France and wins)+P(semi with England and wins)+P(semi with France and Croatia)=(1/3)*0.4+(1/3)*0.6+(1/3)*0.4=0.4667
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