There are a few ways to tackle ths problem. You are given that,
Where
You are required to find
If
Now as
I think I know the answer but would like to hear the forum's answer. What was the logic was in getting at the answer? Also, I copy pasted this from an actual exam so no need to wonder if there was a typo or anything.
The Question:
The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35%. Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work. Determine the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.
(A) 0.05
(B) 0.12
(C) 0.18
(D) 0.25
(E) 0.35
Thank you. That is the answer I got and you just won me lunch from my stubborn friend. And thanks for showing the proof. I was trying to explain the logic in words and was having a hard time getting through.
Several people I showed this to, including my friend, picked .12 (30% * 40%) because they were thinking,
P(A) = 30%
P(B) = 40%
So, P(A and B) = P(A) * P(B)
Obviously, 0.12 was the trap answer for those not thinking it through.
By the way, is this formula correct? If so, why doesn't it work in this problem?