# Thread: probability with multiple factors

1. ## probability with multiple factors

Hi, this question is another one that I can't seem to arrive at a correct answer on.
Suppose that you're thinking about buying a used R-car at Honest Abe's. In order to make an informed decision you look up the records in an auto magazine and find that 30% of these cars have a faulty transmission. To get more information you hire a mechanic who is excellent: Of all the faulty cars he has examined in the past he correctly judged that 90% were "faulty" and only erroneously judged 10% as "OK." He's almost as good at judging good cars: Of all the good cars he's correctly judged that 80% were "good" and only erroneously judged 20% as "faulty."

What is the probability that the R-car you're thinking of buying has a faulty transmission if the mechanic judges it to be "faulty"?

a. .72

b. .80

c. .16

d. .66

e. .30

I feel like I'm doing the math as is it was described in the lecture but I'm not coming up with answers that are options in the multiple choice.

(c) 0.165

3. ## Re: probability with multiple factors

Can you explain to me how you got to that solution. I'm trying to actually understand the math so I can do it on my own.

4. ## Re: probability with multiple factors

Probabilities of:

mf = mechanic says car is faulty
f = car is faulty

$P(\text{mf})=\frac{.90+.20}{.90+.10+.20+.80}=.55$

$P(f)=.30$

Then the conditional prob(car=faulty when mech says faulty):

$P(f|\text{mf})=.55*.30=.165$

5. ## Re: probability with multiple factors

Thanks again, this makes a lot more sense now, I'm pretty sure I had the matrix setup backwards.