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Sagot :
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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