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Answer:

What is the probability of getting a vowel (a success) for the spinner shown?

✔ 1/3

Suppose you spin the spinner 5 times.

✔ P(3 successes) means “the probability of getting a vowel on exactly 3 of the spins.”

Step-by-step explanation:

edg 2020

Using the binomial distribution, it is found that:

  • The probability of a success is of 1/3.
  • P(X = 3) = 0.1646.

For each spin, there are only two possible outcomes, either it is a vowel, or it is not. The result of a spin is independent of any other spin, hence the binomial distribution is used to solve this question.

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:

  • The spinner has 3 regions, A, B and C, one of which is a vowel, hence p = 1/3 = 0.3333.
  • There will be 5 spins, hence n = 5.

The probability of 3 successes is given by:

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

[tex]P(X = 3) = C_{5,3}.(0.3333)^{3}.(0.6667)^{2} = 0.1646[/tex]

More can be learned about the binomial distribution at https://brainly.com/question/14424710

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