Respuesta :
Using the binomial distribution, it is found that the expected score of the game is of 21.
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q successes is:
[tex]E_s(X) = \frac{q}{p}[/tex]
In this problem, a die has a p = 1/6 probability of resulting in a 1, hence the expected number of trials is:
[tex]E_s(X) = \frac{1}{\frac{1}{6}} = 6[/tex]
In each trial, each outcome from 1 to 6 is equally as likely, hence the expected score of a single trial is given by:
[tex]E = \frac{1 + 6}{2} = 3.5[/tex]
Then, the expected score of the six trials is:
6 x 3.5 = 21.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
