1. ## Intro probability question

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?

2. Originally Posted by vexiked
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
$P(\mathcal{U}|\mathcal{A})=\frac{ P(\mathcal{U}\mathcal{A})}{ P(\mathcal{A})}=\frac{ P(\mathcal{A}|\mathcal{U})P(\mathcal{U})}{ P(\mathcal{A})}$

3. Originally Posted by tedii
Here I think it is simplest to name a few different stats.
.40 jobs are done by A
.60 jobs are not done by A
.10 jobs are not satisfactory
.90 jobs are satisfactory
P(unsatisfactory given A)=.4 x .1 = .04
P(satisfactory given A)= .4 x .9 = .36
Which if you look at those add up to 40 percent which makes sense, since plumber A did a total of 40 percent of those jobs.
There are some serious flaws with the above.
Note that "Half the complaints dealt with plumber A".
Where is that fact considered?

4. I apologize I shouldn't do this while I'm at work I guess. Sometimes I read to quickly and miss points. I will look again in just a bit.

5. 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).

6. Thank you for your help