Which of the following is written as a rational function

In a string of 12 Christmas tree light bulbs, 3 are defective. The bulbs are selected at random and tested, one at a time, until

Juliette [100K]

Using the hypergeometric distribution, it is found that there is a 0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

In this problem, the bulbs are chosen without replacement, hence the <em>hypergeometric distribution</em> is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

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

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

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 12 bulbs, hence N = 12.

3 are defective, hence k = 3.

The third defective bulb is the fifth bulb if:

Two of the first 4 bulbs are defective, which is P(X = 2) when n = 4.

The fifth is defective, with probability of 1/8, as of the eight remaining bulbs, one will be defective.

Hence:

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

$P(X = 2) = h(2,12,4,3) = \frac{C_{3,2}C_{9,1}}{C_{12,4}} = 0.2182$

0.2182 x 1/8 = 0.0273.

0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

More can be learned about the hypergeometric distribution at brainly.com/question/24826394

8 0

1 year ago

Solve for y: 1.7-(3+2.4y) = 4(3y-2.91)

frez [133]

1.7-3-2.4y= 12y-11.64

-1.3-2.4y = 12y - 11.64

-2.4y = 12y - 11.64

-14.4y = -10.34

y= 10.34/14.4= 5.17/7.20 or 517/720

6 0

2 years ago

What is the value of s in the equation 3r = 10 + 5s, when r = 10?

kupik [55]

S = 4

3(10) = 10 + 5s
30 = 10 + 5s
30 - 10 = 5s
20 = 5s
20 ÷ 5 = s
4 = s

4 0

2 years ago

Read 2 more answers

Asa has 4 colored pencils. His friend purchases three times as many. If Asa’s friend buys two more 4-packs, which expression sho

daser333 [38]

24

Three times as many as four - 3(4) / 4*3/ 4+4+4

4 x 3 = 12

Then for 2 more 4 packs, it'd be 8 since it's either 2*4 or 4+4 (both equal eight)

And then you'd add them both together, 12+8=20

But since it's asking for both Asa and his friend's total amount, you'd add four more to it since 20 is just his friend's amount.

5 0

2 years ago

in a fundraiser, Mrs. Smith pledges $1 for each mile walked . if Sam walks 20 miles how much will Mrs. Smith donate? what is yhe

EleoNora [17]

Mrs. Smith donated $20
The constant proportionality is $1 because no matter what, Mrs. smith will donate $1 for each mile. So if Sam were to only walk 1 mile, mrs. smith would donate $1. Or seen as a 1:1 proportion.

5 0

2 years ago