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An English teacher has equal numbers of fiction, literature, and poetry books. Each day, she randomly selects one book to read from. She designs a simulation to estimate the probability that the next three books she selects are all literature. Which simulation design could she use to estimate the probability?​

Sagot :

Using probability concepts, it is found that she could use a binomial distribution with [tex]n = 3[/tex] and [tex]p = \frac{1}{3}[/tex] to estimate the probability that the next three books she selects are all literature.

For each book she selects, there are only two possible outcomes, either it is a literature book, or it is not. The probability of a book selected being a literature book is independent of any other book, 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:

  • Next three books selected, hence [tex]n = 3[/tex].
  • She has an equal number of fiction, literature, and poetry books, hence, the probability of each book selected being a literature book is [tex]p = \frac{1}{3}[/tex]

Hence, she could use a binomial distribution with [tex]n = 3[/tex] and [tex]p = \frac{1}{3}[/tex] to estimate the probability that the next three books she selects are all literature.

You can learn more about the binomial distribution at https://brainly.com/question/24863377

Answer:

Number Cube

Let 1, 6= Literature

Let 2, 4= Fiction

Let 3, 5= Poetry

Roll the cube 3 times, Repeat

It has to be equal probability for all three

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