Using the binomial distribution, it is found that there is a [tex]\frac{7}{8}[/tex] probability that at least one of the coins comes up heads.
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:
- A coin is fair, hence p = 1/2.
- Three coins are thrown, hence n = 3.
The probability that at least one of the coins comes up heads is given by:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.\left(\frac{1}{2}\right)^{0}.\left(\frac{1}{2}\right)^{3} = \frac{1}{8}[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = \frac{8}{8} - \frac{1}{8} = \frac{7}{8}[/tex]
[tex]\frac{7}{8}[/tex] probability that at least one of the coins comes up heads.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ2
