Answer:
0.6786
0.3214
1 / 172
171 / 172
Step-by-step explanation:
Note: The tree diagram is attached below.
a) The athlete is a drug user, given that the test is positive P(D/+)
Using conditional Probability:
P ( D / + ) = P ( D and + ) / P ( +)
= (0.1 * 0.95) / (0.1 * 0.95 + 0.9*0.05)
= 0.6786
Answer: P ( D / + ) = 0.6786
b) The athlete is not a drug user, given that the test is positive P(D' / + )
Using conditional Probability:
P ( D' / + ) = P ( D' and + ) / P (+)
= (0.9 * 0.05) / (0.1 * 0.95 + 0.9*0.05)
= 0.3214
Answer: P ( D' / + ) = 0.3214
c) The athlete is a drug user, given that the test is negative P (D / - )
Using conditional Probability:
P ( D / - ) = P ( D and - ) / P (-)
= (0.1 * 0.05) / (0.9 * 0.95 + 0.1*0.05)
= 1 / 172
Answer: P ( D / - ) = 1 / 172
(d) The athlete is not a drug user, given that the test is negative P (D' / - )
Using conditional Probability:
P ( D' / - ) = P ( D' and - ) / P (-)
= (0.9 * 0.95) / (0.9 * 0.95 + 0.1*0.05)
= 171 / 172
Answer: P ( D / - ) = 171 / 172
