Using the binomial distribution, it is found that there is a 0.125 = 12.5% probability that the team goes to the championship.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- His team has a p = 0.5 probability of winning each game.
- The team plays 3 games, hence n = 3.
The team moves to the championship if they win all three games, hence the probability is P(X = 3), given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125[/tex]
0.125 = 12.5% probability that the team goes to the championship.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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