Answer:
The probability that Swallows will win the trophy is 0.8064
The probability that Rucks will win the trophy is 0.1936
Step-by-step explanation:
For each game, there are only two possible outcomes. Either the Swallows win, or they do not. The probability of them winning a game is independent of any other game, which means that the binomial probability distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Probability the Swallows wins is 0.56
This means that
2 games:
This means that
The probability that Swallows will win the trophy is
Probability they win at least one game, so:
In which
Then
0.8064 = 80.64% probability the Swallows win the trophy and 0.1936 probability that the Rucks win the trophy.