Respuesta :
Using the binomial distribution, it is found that there is a 0.3472 = 34.72% probability that it comes up five exactly once.
For each dice that is rolled, there are only two possible outcomes, either it comes up 5, or it does not. The probability of a dice coming up 5 is independent of any other dice, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[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:
- There are three throws, hence [tex]n = 3[/tex].
- A five is one of the six sides, hence [tex]p = \frac{1}{6} = 0.1667[/tex]
The probability that it comes up five exactly once is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.1667)^{1}.(0.8333)^{2} = 0.3472[/tex]
0.3472 = 34.72% probability that it comes up five exactly once.
A similar problem is given at https://brainly.com/question/24863377
