Using the binomial distribution, it is found that there is a 0.3125 = 31.25% probability of getting 2 goals out of 5.
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.
The values of the parameters are given as follows:
n = 5, x = 2, p = 0.5.
Hence the probability is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]
0.3125 = 31.25% probability of getting 2 goals out of 5.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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