Using the binomial distribution, it is found that there is a 0.037 = 3.7% probability that Adina's friend correctly identifies each of the 3 cups of water.
For each water, there are only two possible outcomes, either it is correctly identified, or it is not. The probability of a water being correctly identified is independent of any other water, hence the binomial distribution is used to solve this question.
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:
In this problem:
The probability that each of the 3 cups is correctly identified is P(X = 3), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.3333)^{3}.(0.6667)^{0} = 0.037[/tex]
0.037 = 3.7% probability that Adina's friend correctly identifies each of the 3 cups of water.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
