Six Lions. Please mark this as brainliest answer
Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.
The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.
<h3>What is the hypergeometric distribution formula?</h3>
The formula is:
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7DC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
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 is a total of 3 + 4 = 7 marbles, hence N = 7.
- Of those, 3 are blue, hence k = 3.
- 2 marbles will be taken, hence n = 2.
The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7DC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
![P(X = 0) = h(0,7,2,3) = \frac{C_{3,0}C_{4,2}}{C_{7,2}} = 0.2857](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20h%280%2C7%2C2%2C3%29%20%3D%20%5Cfrac%7BC_%7B3%2C0%7DC_%7B4%2C2%7D%7D%7BC_%7B7%2C2%7D%7D%20%3D%200.2857)
![P(X = 2) = h(2,7,2,3) = \frac{C_{3,2}C_{4,0}}{C_{7,2}} = 0.1429](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20h%282%2C7%2C2%2C3%29%20%3D%20%5Cfrac%7BC_%7B3%2C2%7DC_%7B4%2C0%7D%7D%7BC_%7B7%2C2%7D%7D%20%3D%200.1429)
Hence:
![p = P(X = 0) + P(X = 2) = 0.2857 + 0.1429 = 0.4286](https://tex.z-dn.net/?f=p%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%202%29%20%3D%200.2857%20%2B%200.1429%20%3D%200.4286)
0.4286 = 42.86% probability of getting 2 of the same colour.
You can learn more about the hypergeometric distribution at brainly.com/question/4818951
3 and 1 are the factors of 3 duhhh lol
Answer:
c. 6√2
Step-by-step explanation:
The step by step explanation is shown in the picture above
Brainliest? The outcome of the second selection is not affected in any way by the outcome of the first selection. Therefore the events are independent.