Mathematics, 04.07.2019 11:20 emm16045

The probability that a given computer chip will fail is 0.02. find the probability that of 5 delivered chips, exactly 2 will fail.

Answers: 1

Show answers

Answers

Probability of an event is the measure of its chance of occurrence. The probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

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

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

For the given case, as failing or working of chips usually doesn't depend on other chips' working condition, so they're independent(assuming). There are two cases for each chip's working(random experiment) that it is either working or failed.

If we take Success of the considered binomial experiment(working status of chip) = Chip working fine

Then, as per given data, we have

P(chip working fine ) = 1 - P(chip not working) = 1 - 0.02 = 0.98 = Probability of success in Bernoulli experiment (chip's working status).

There are n = 5 chips, p = probability of success = 0.98, q = 1-p = 0.02

If we take X = number of chips of of 5 chips working, then:

$X \sim B(n = 5, p = 0.98)$

Then, the needed probability is P(Exactly two chips fail) = P(Exactly 5-2 = 3 chips work) = P(X = 3)

And thus, the needed probability is calculated as:

$P(X = 3) = \: ^5C_3(0.98)^3(0.02)^2 = \dfrac{5.4.3}{3.2.1} \times 0.941192 \times 0.0004 = 0.003764768$

(using the probability mass function of binomial distribution).

Thus, the probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

Learn more about binomial distribution here:

link

Answer from: daytonalive6511

Since the chip either passes or fails, this problem is one in binomial probability, with p(fail)=0.02 and n=5.

If your calculator features probability functions such as binompdf(n, p), use it.
Mine is a TI-83 Plus.

The probability that exactly two chips will fail is

binompdf(5,0.02,2) = 0.0038. This is quite a small probability.

Answer from: Quest

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

Answer from: Quest

Answer: the correct answer is 10step-by-step explanation: let the number be n, then the expression becomes,then“twelve more than the quotient of a number and two, decreased by four” is $(\frac{n}{2}+12)-4$ when n=4,we substitute 4 whetever we see n to get, $(\frac{4}{2}+12)-4$ we simplify to obtain, $=(2+12)-4$ we further simplify to get, $=14-4=10$ therefore the correct answer is c.

Another question on Mathematics

Mathematics, 21.06.2019 16:30

What is the difference between regular convex and concave polygons

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Aquadratic equation in standard from is written ax^2= bx+c, where a,b and c are real numbers and a is not zero?

Answers: 1

Answer

Mathematics, 22.06.2019 05:30

Consider the function f left parenthesis x right parenthesis equals 4 x squared minus 3 x minus 1f(x)=4x2−3x−1 and complete parts (a) through (c). (a) find f left parenthesis a plus h right parenthesis f(a+h); (b) find startfraction f left parenthesis a plus h right parenthesis minus f left parenthesis a right parenthesis over h endfraction f(a+h)−f(a) h; (c) find the instantaneous rate of change of f when aequals=77.

Answers: 3

Answer

You know the right answer?

The probability that a given computer chip will fail is 0.02. find the probability that of 5 deliver...

Questions

Mathematics, 04.06.2020 22:59

If f(x)= 3x^2-2x+4.and g(x)= 5x^2 +6x -8find(f-g)(x)...