The question asks the student to find a conditional probability (often reversing the conditioning direction) using Bayes' theorem or the definition of conditional probability after constructing or using a tree.
The Spanish national team will compete in the 2023 FIFA Women's World Cup. In the first two matches of the group stage, which consists of three matches, the probability of winning each one is 80\%. However, due to increased morale among the players, if they win the first two matches, the probability of winning the third rises to 90\%. Otherwise, the probability of winning the third match remains at 80\%. It is requested: a) ( 0.5 points) Determine the probability that the Spanish national team does not win any match during the group stage. b) (1 point) Calculate the probability that the national team wins the third match of the group stage. c) (1 point) If we know that the national team has won the third match, determine the probability that they did not win one of the two previous matches.