When the Bucks play Chiefs at football, the probability that the Chiefs, on present form, will win is 0.56. In a competition, these teams are to play two more pgames. If Swallows beats Bucks in at least4one of these games, they will win the competition, otherwise Bucks will win the trophy. NB: Round off to 2 decimal places. a. The probability that Swallows will win the trophy is [a] probability that Rucks will win the trophy is

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.