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Milani's teacher draws students names at random, calls on the student, and replaces the name so that students know they should always be prepared to respond. There are 202020 students in Milani's class. Let XXX be the number of names it takes for the teacher to draw Milani's name.
Find the probability that the teacher first draws Milani's name as the 7^{\text{th}}7
th
7, start superscript, start text, t, h, end text, end superscript name.
You may round your answer to the nearest hundredth.
P(X=7)=P(X=7)=

Respuesta :

Using the binomial distribution, it is found that there is a 0.0368 = 3.68% probability that the teacher first draws Milani's name as the 7th student.

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 20 students, hence in each question the probability that Milani's name is called is p = 1/20 = 0.05.

The probability that the teacher first draws Milani's name as the 7th student is P(X = 0) when n = 6(none during the first six) multiplied by 0.05(called during the seventh), hence:

P(X = 7) = (0.95)^6 x 0.05 = 0.0368.

0.0368 = 3.68% probability that the teacher first draws Milani's name as the 7th student.

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

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