Mathematics, 17.07.2019 02:10 raquelqueengucci25

Suppose that a classroom has 8 light bulbs. the probability that each individual light bulb works is 0.8. suppose that each light bulb works independently of the other light bulbs. what is the probability that all eight of the light bulbs work?
a.0.17
b.0.13
c.0.1024
d.0.8

Answers: 1

Show answers

Answers

Answer from: orlando19882000

You can use binomial distribution, and thus, its probability function to find the needed probability.

The probability that all eight of the light bulbs work is 0.167

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

$X \sim B(n,p)$

The probability that out of n trials, there'd be x successes is given by

$P(X =x) = \: ^nC_xp^x(1-p)^{n-x}$

Using the above method to find the needed probability

Since all the light bulbs' working is independent, and each bulb's chance of working is 0.8 and there are 8 bulbs, thus,

n = 8

p = 0.8

and Let X be a random variable tracking how many out of 8 bulbs are working, then we have:

$X \sim B(8, 0.8)$

Then, the needed probability is P(X = 8) (since we need to know probability that all 8 bulbs will work)

By using the probability mass function of binomial distribution, we get:

$P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\\P(X = 8) = \:^8C_8(0.8)^8(1-0.8)^{8-8} = 1 \times (0.8)^8 \times 1 \approx 0.167$

Thus,

The probability that all eight of the light bulbs work is 0.167

Learn more about binomial distribution here:

link

Answer from: nacho5317

a. 0.17

Step-by-step explanation:

Total number of light bulbs = 8

The probability that each individual light bulb works = 0.8

The working of light bulbs is independent of each other, this means one light bulb does not influence the other light bulbs.

We need to calculate the probability that all eight of the light bulbs work. Since the light bulbs work independently, the overall probability of independent events occurring together is the product of their individual probabilities. Therefore,

Probability that all eight of the light bulbs work = 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8

= $(0.8)^{8}$

= 0.16777216

≈ 0.17

Thus, option a gives the correct probability that all eight of the light bulbs work

Answer from: Quest

whose power in the senate is equal to the power of the speaker of the house?

step-by-step explanation:

Answer from: Quest

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves

What is the slope of a line that is parallel to the line shown? taking quiz need

Another question on Mathematics

Mathematics, 21.06.2019 12:30

Marie drew the triangle shown. she wants to draw a second triangle that is different from this one. use the drop-down menus below to complete the statements about the second triangle.

Answers: 1

Answer

Mathematics, 21.06.2019 15:00

1. are the triangles similar and if so why? what is the value of x? show your work.

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

Which inequality has a dashed boundary line when graphed ?

Answers: 2

Answer

Mathematics, 21.06.2019 21:50

Desmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? \ 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2x

Answers: 3

Answer

You know the right answer?

Suppose that a classroom has 8 light bulbs. the probability that each individual light bulb works is...

Questions