At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
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
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] 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
[tex]p = 0.95*0.08 + 0.87*0.17 + 0.11*0.75 = 0.3064[/tex]
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 [tex]P(A) = 0.3064[/tex]
Probability of testing positive while never using the drug.
11% of 75%. So
[tex]P(A \cap B) = 0.11*0.75 = 0.0825[/tex]
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0825}{0.3064} = 0.2693[/tex]
0.2693 = 26.93% probability that this drug user never used the prohibited drug.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.