Question

In: Statistics and Probability

You can purchase a certain type of resistor from supplier X, Y or Z. The probability...

You can purchase a certain type of resistor from supplier X, Y or Z. The probability of having a faulty resistor if the resistor was bought from supplier X is 0.02; from supplier Y is 0.05; and from supplier Z is 0.1. Your company purchased a total of 1000 resistors: 300 from supplier X, 500 from supplier Y, and 200 from supplier Z. Use this information to answer the following questions.

1.What is the probability that a randomly selected resistor was purchased from supplier Y?(round to 3 decimals)

2.What is the probability that a randomly selected resistor was purchased from supplier X and is faulty? (round to 3 decimals)

3.What is the probability that a randomly selected resistor is faulty? (round to 3 decimals)

4.What is the probability that a randomly selected resistor is not faulty? (round to 3 decimals)

5.Given that a randomly selected resistor is faulty, what is the probability that it was purchased from supplier Y? (round to 3 decimals)

Solutions

Expert Solution

solution :

total purchases resistors = 1000

purchases from X = 300

from Y = 500

from z = 200

probabilty of defective from X = 0.02, from Y = 0.05, from z =0.1

first of all preparing an contingency table with the given information

faulty not faulty total
X 300*0.02 = 6 294 300
Y 500*0.05 = 25 475 500
Z 200*0.1 = 20 180 200
total 51 949 1000

1)

total resistor purchases from supplier Y = 500

so probability of randomly selected resistor purchases from supplier Y = 500/1000 = 0.5

2)

number of resistor purchases from supplier X and whcich are faulty = 6

so P( purchases from X and faulty ) = 6/1000 = 0.006

3)

total number of resistor which are faulty = 51

so P( faulty ) = 51/1000 = 0.051

4)

total number of resistors which are not faulty = 949

so, P( not faulty ) = 949/1000 = 0.949

5)

it is given that the selected resistor is faulty we have to find the probabilty that it was purchased from Y

total number of faulty resistors = 51

number of faulty resistors in Y = 25

so P(purchases from Y | it is faulty ) = 25/51 = 0.49


Related Solutions

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...
The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just f (because f is already curried) let f x y z = (x,(y,z)) let f x y z = x (y z)
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z)...
If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z) b. X×(Y×Z) = (X.Z)Y – (X.Y)Z c. X.(Y×Z) = -Y.(X×Z)
Digital Logic Simplify: F = (x’∙ y’∙ z’) + (x’∙ y ∙ z’) + (x ∙...
Digital Logic Simplify: F = (x’∙ y’∙ z’) + (x’∙ y ∙ z’) + (x ∙ y’ ∙ z’) + (x ∙ y ∙ z) F = (x + y + z’) (x + y’ + z’) (x’ + y + z’) (x’ + y’ + z)
A retailer purchases a certain type of chemical from a supplier on the following quantity discount...
A retailer purchases a certain type of chemical from a supplier on the following quantity discount schedule: • If the order amount is less than 100 kg.s, the supplier charges $30 per kg. • If the order amount is at least 100 kg.s and less than 500 kg.s, the supplier applies an incremental discount where the first 100 kg. costs $30 per kg. and the remaining amount costs $28 per kg. • If the order amount is at least 500...
Use two different ways to prove X Y + Z = (X + Z)(Y + Z)....
Use two different ways to prove X Y + Z = (X + Z)(Y + Z). a) Use pure algebraic way b) k-maps
For each of the formulas below, state whether it is true or false. a) pX,Y,Z(x,y,z)=pY(y)pZ∣Y(z∣y)pX∣Y,Z(x∣y,z)   ...
For each of the formulas below, state whether it is true or false. a) pX,Y,Z(x,y,z)=pY(y)pZ∣Y(z∣y)pX∣Y,Z(x∣y,z)       Select an option         True         False    b) pX,Y∣Z(x,y∣z)=pX(x)pY∣Z(y∣z)       Select an option         True         False    c) pX,Y∣Z(x,y∣z)=pX∣Z(x∣z)pY∣X,Z(y∣x,z)       Select an option         True         False    d) ∑xpX,Y∣Z(x,y∣z)=1       Select an option         True         False    e) ∑x∑ypX,Y∣Z(x,y∣z)=1       Select an option         True   ...
Find ??, ?? and ?? of F(x, y, z) = tan(x+y) + tan(y+z) – 1
Find ??, ?? and ?? of F(x, y, z) = tan(x+y) + tan(y+z) – 1
Let f : X → Y and g : Y → Z be functions. We can...
Let f : X → Y and g : Y → Z be functions. We can define the composition of f and g to be the function g◦ f : X → Z for which the image of each x ∈ X is g(f(x)). That is, plug x into f, then plug theresultinto g (justlikecompositioninalgebraandcalculus). (a) If f and g arebothinjective,must g◦ f beinjective? Explain. (b) If f and g arebothsurjective,must g◦ f besurjective? Explain. (c) Suppose g◦ f isinjective....
Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2*y+z=0. find the extreme value of f(x,y,z)...
Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2*y+z=0. find the extreme value of f(x,y,z) and determine whether it is maximum of minimum.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT