Using the binomial distribution, it is found that the probability of getting 3 heads is of [tex]\frac{8}{125}[/tex].
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, we have that when n = 3, [tex]P(X = 3) = \frac{27}{125}[/tex], hence:
[tex]p^3 = \frac{27}{125}[/tex]
[tex]p = \sqrt[3]{\frac{27}{125}}[/tex]
[tex]p = \frac{3}{5}[/tex]
The probability of 3 heads is P(X = 0), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.\left(\frac{3}{5}\right)^{0}.\left(\frac{2}{5}\right)^{3} = \frac{8}{125}[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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