Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
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
#SPJ1
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
