Answer:
a) 0.3064 = 30.64% probability that athlete will test positive for prohibited drug use.
b) 0.2693 = 26.93% probability that this drug user never used the prohibited drug.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
A. If an athlete is selected at random, what is the probability that athlete will test positive for prohibited drug use?
100 - 5 = 95% of 8%
100 - 13 = 87% of 17%
11% of 75%
So
0.3064 = 30.64% probability that athlete will test positive for prohibited drug use.
B. If an athlete tests positive after a drug test, what is the probability that this drug user never used the prohibited drug?
Conditional Probability
Event A: Tests Positive
Event B: Never used the drug.
0.3064 = 30.64% probability that athlete will test positive for prohibited drug use
This means that
Probability of testing positive while never using the drug.
11% of 75%. So
0.2693 = 26.93% probability that this drug user never used the prohibited drug.