IDNLearn.com: Your one-stop destination for finding reliable answers. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.
Sagot :
Using the hypergeometric distribution, it is found that there is a 0.1515 = 15.15% probability that you pick at least 3 green balls.
The balls are chosen without replacement, hence the hypergeometric distribution is used.
What is the hypergeometric distribution formula?
The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There are 4 + 5 + 3 = 12 balls, hence N = 12.
- 5 of the balls are green, hence k = 5.
- 4 balls will be picked, hence n = 4.
The probability that you pick at least 3 green balls is:
[tex]P(X \geq 3) = P(X = 3) + P(X = 4)[/tex]
Hence:
[tex]P(X = 3) = h(3,12,4,5) = \frac{C_{5,3}C_{7,1}}{C_{12,4}} = 0.1414[/tex]
[tex]P(X = 4) = h(4,12,4,5) = \frac{C_{5,4}C_{7,0}}{C_{12,4}} = 0.0101[/tex]
Then:
[tex]P(X \geq 3) = P(X = 3) + P(X = 4) = 0.1414 + 0.0101 = 0.1515[/tex]
0.1515 = 15.15% probability that you pick at least 3 green balls.
You can learn more about the hypergeometric distribution at https://brainly.com/question/4818951
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.
