Respuesta :
Using the binomial distribution, it is found that the probability of winning this game of chuck a luck is:
b. 0.421
For each roll of the dice, there are only two possible outcomes, either the value you bet appears, or it does not. The results of each roll are independent, hence, 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:
- For each roll, there are 6 numbers, you bet 1, hence [tex]p = \frac{1}{6} = 0.1667[/tex]
- The dice is rolled 3 times, hence [tex]n = 3[/tex].
The probability of winning is:
[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}.(0.1667)^{0}.(0.8333)^{3} = 0.579[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.579 = 0.421[/tex]
Option b is correct.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
