Answer :

Using the binomial distribution, it is found that there is a 0.16 = 16% probability of choosing a gray button, replacing it, and choosing gray again.

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 two trials, hence n = 2.
  • Two out of the five buttons are gray, hence p = 2/5 = 0.4.

The probability of two gray buttons is:

P(X = 2) = (0.4)² = 0.16.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

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