Respuesta :
Using the binomial distribution, it is found that there is a 0.9844 = 98.44% probability that bohan goes to café georgia for a coffee today.
For each friend, there are only two possible outcomes, either they go to the cafe, or they do not. The probability of a friend going to the cafe is independent of any other friend, hence, the binomial distribution is used to solve this question.
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:
- There are 3 friends, hence n = 3.
- They all go to the cafe with a 3/4 probability, hence p = 3/4 = 0.75.
The probability at least one goes 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}.(0.75)^{0}.(0.25)^{3} = 0.0156[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0156 = 0.9844[/tex]
0.9844 = 98.44% probability that bohan goes to café georgia for a coffee today.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
