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7. At a fair, Evie gets five darts she can toss at balloons. If there is a probability of that any given dart she
10
throws will hit a balloon, independent of her other throws, which of the following is closest to the probability
she will hit at least one balloon with her five darts?
(1) 41%
(3) 54%
(2) 50%
(4) 62%

Respuesta :

Using the binomial distribution, it is found that the probability she will hit at least one balloon with her five darts is:

(1) 41%.

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, we have that:

  • The probability of a single dart hitting is of p = 1/10 = 0.1.
  • She will throw five darts, hence n = 5.

The probability of hitting at least one is given by:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

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

[tex]P(X = 0) = C_{5,0}.(0.1)^{0}.(0.9)^{5} = 0.59[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.59 = 0.41[/tex]

Which means that option 1 is correct.

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

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