SOLUTION: three contractors a b c have constructed buildings in a society in which 2%3%and 4% of the buildings constructed respectively by a b c have water leakage in the building if they ha

Algebra.Com
Question 1203530: three contractors a b c have constructed buildings in a society in which 2%3%and 4% of the buildings constructed respectively by a b c have water leakage in the building if they have constructed 50%30%20% of the buildings in a society respectively a building is selected and found that it has water leakage interpret which contractor would you guess did construct the building


Answer by ikleyn(52878)   (Show Source): You can put this solution on YOUR website!
.
three contractors a b c have constructed buildings in a society in which 2%3%and 4% of the buildings
constructed respectively by a b c have water leakage in the building if they have constructed 50%30%20%
of the buildings in a society respectively a building is selected and found that it has water leakage
interpret which contractor would you guess did construct the building
~~~~~~~~~~~~~~~~~~~~~~


        Your writing/printing is terrible.
        I will not edit it, since I just tired to edit after visitors.


This problem is about conditional probability.

They want you find three conditional probabilities 

    P(leakage is from A given that there is a leakage)

    P(leakage is from B given that there is a leakage)

    P(leakage is from C given that there is a leakage)


then compare these values and select the maximum of the three.


    P(leakage is from A given that there is a leakage) =  = 0.3704,


    P(leakage is from B given that there is a leakage) =  = 0.3333,


    P(leakage is from C given that there is a leakage) =  = 0.2963.


Of these three probabilities, the greatest is from A; so, we can suspect that the leakage is from A.


The structure of these formulas is the same: the denominator is the probability 
having a leakage (from any of the three buildings);
the numerators are individual probabilities having leakage from A, B, or C, respectively.


Since the denominator is the same in all three formulas, we could cut down our calculations for this problem
by computing the numerators only.


But I did the full job in order for the interior logic be CLEAR for the reader.

Solved, with complete explanations.



RELATED QUESTIONS

Five of 10 new buildings in a city violate the building code. A random sample of three... (answered by Boreal,math_tutor2020,ikleyn)
Five of 10 new buildings in a city violate the building code. A random sample of three... (answered by ikleyn)
b. Hospital records show that 75% of the patients will recover from a certain disease.... (answered by ewatrrr)
Student painters which specialize in painting the exterior of residential buildings have... (answered by ikleyn)
The time, T days, needed to paint some buildings is directly proportional to the number... (answered by josgarithmetic)
The local historical society wants to preserve two buildings. The total age of the... (answered by greenestamps)
The buildings in a factory depreciate at the rate of 2.5% per year. Hence the value A of... (answered by Theo)
To obtain a pleasing rectangular shape, the ancient Greeks constructed buildings with a... (answered by Theo)
Please help me solve this word problem: Two of the tallest buildings in the world are... (answered by CubeyThePenguin)