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A division of a company has over 200 employees, 40% of which are male. The company is going to
randomly select 4 of these employees to attend a conference. Let X = the number of male employees
chosen.
What is the probability that exactly 3 of the 4 employees chosen are male?
You may round your answer to the nearest hundredth.
P(X = 3
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4804097745

Answer:

0.15

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0.1536 = 15.36% probability that exactly 3 of the 4 employees chosen are male.

For each employee, there are only two possible outcomes, either they are male, or they are not. The probability of an employee being male is independent of any other employee, 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:

  • 40% of the employees are male, hence [tex]p = 0.4[/tex].
  • 4 of these employees are randomly selected, hence [tex]n = 4[/tex].

The probability that exactly 3 of the 4 employees chosen are male is P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{4,3}.(0.4)^{3}.(0.6)^{1} = 0.1536[/tex]

0.1536 = 15.36% probability that exactly 3 of the 4 employees chosen are male.

To learn more about the binomial distribution, you can check https://brainly.com/question/24863377

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