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

2 years ago

Evaluate using the given values<br> b=1, c=2, d=3, p=-3, q=-2, r=-1<br> a) 2b+c-d

IRISSAK [1]

The answer should be one

5 0

3 years ago

Help me plsssssssssssss

OLEGan [10]

Answer:

bro the co ordinates are in the picture itself

7 0

3 years ago

Read 2 more answers

Latonya bought flowers for her mother. She spent $45. Each tulip was $1 and each rose was $2. She bought 3 more tulips than rose

Yuliya22 [10]

Lets start from scratch.
45 is the number of money she spent that means that right side of = sign is 45
let m represents number of roses.
we can write:

t*$1+ m*$2 = $45

Since she bought 3 more tulips than roses that means that m = t - 3

when we express m we get:

t + 2*(t-3) = 45

<span>the answer is B.

-Lampa20</span>

8 0

3 years ago