Please please help me!

g An urn contains 150 white balls and 50 black balls. Four balls are drawn at random one at a time. Determine the probability th

xxTIMURxx [149]

Answer:

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

Step-by-step explanation:

For sampling with replacement, we use the binomial distribution. Without replacement, we use the hypergeometric distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Sampling with replacement:

I consider a success choosing a black ball, so $p = \frac{50}{150+50} = \frac{50}{200} = 0.25$

We want 2 black balls and 2 white, 2 + 2 = 4, so $n = 4$ , and we want P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{4,2}.(0.25)^{2}.(0.75)^{2} = 0.2109$

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Sampling without replacement:

150 + 50 = 200 total balls, so $N = 200$

Sample of 4, so $n = 4$

50 are black, so $k = 50$

We want P(X = 2).

$P(X = 2) = h(2,200,4,50) = \frac{C_{50,2}*C_{150,2}}{C_{200,4}} = 0.2116$

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

3 0

3 years ago

Someone plzz help meeeee thank youuu

Vikentia [17]

Answer:

The answers a ! Hope this helps

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

2x divided by x+5 less than or equal to 0

coldgirl [10]

It is more than 0, because you cancel the x, and you get 2+5, which is 7

4 0

3 years ago

25 people apply for a job, 15 men and 10 women. they will hire 10 people, with 40% of them women. how many different staff selec

luda_lava [24]

So if they'll hire 40% women, and they're hiring 10 people, this means that they'll hire 4 women. And the rest of the people are all men, or 6 of them.

So basically, you can think of this like a tree, taking the men's side first, with 15 possible hires in the beginning, and then 14 more stemming off of that, and then 13 more stemming of those, etc.

So basically it would be:

15 * 14 * 13 * 12 * 11 * 10

Because there are four spots for men, and there were 15 men, and after every hire, there will be one less applicant, because there would've been one hire instead.

So;

15 * 14 * 13 * 12 * 11 * 10 = 3603600

And then women just do the same thing.

10 * 9 * 8 * 7 = 5040

Then just multiply those together as well.

18162144000 is your final answer.

5 0

3 years ago

12 M cubed minus 22 M squared minus 70 m

Andru [333]

I'm guessing you needed this factored and apologies for the lateness, this popped up after I answered another question.

12m³ - 22m² - 70m

2m(6m² - 11m - 35)
2m(6m² + 10m - 21m - 35)
2m(2m(3m + 5) - 7(3m + 5))

Your factored answer is:

2m(2m - 7)(3m + 5)

3 0

4 years ago

Please please help me!​

Please please help me!