Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Using the binomial distribution, there is a 0.6328 = 63.28% probability that she wins at most 1 prize.
For each box, there are only two possible outcomes, either it has a prize, or it does not. The probability of a box having a prize is independent of any other box, 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:
- She buys 5 boxes, hence [tex]n = 5[/tex]
- 1 in 4 boxes has a prize, hence [tex]p = \frac{1}{4} = 0.25[/tex]
The probability is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]
[tex]P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2373 + 0.3955 = 0.6328[/tex]
0.6328 = 63.28% probability that she wins at most 1 prize.
A similar problem is given at https://brainly.com/question/24863377
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
