The question is:
A survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs in their homes. Half the complaints dealt with plumber A, who does 40% of the jobs. Find Probability of
1) an unsatisfactory job, given the plumber was A
2) a satisfactory job, given the plumber was A.
I think I can solve this by:
P(unsatisfactory given A) = .5 x .4 = .20
P(satisfactory given A) = 1 - .20 = .80
Is this correct?
With the "Given. . ." statement, you are essentially reducing your sample space. Plumber A does 40% of the jobs, so our given is (0.4). This is the space we are drawing from. Now we wish to know, who complained AND was serviced by plumber A. The problem tells us that that P(Someone is dissatisfied AND the work was was done by Plumber A)=0.5.
Thus the P(Unsatisfied|Plumber A)=0.05/04. Note: that 0.10 were dissatisfied with their plumbing work in general, and half of that, 0.05, came from Plumber A, who does a total of 0.4 of the work.
Now, if we want the P(Satisfied|Plumber A), all we need do is take the compliment of part A. which is 1-P(Unsatisfied|Plumber A).