An athletic league does drug testing of its athletes, 10 percent of whom use drugs. this test, however, is only 95 percent reliable. that is, a drug user will test positive with probability 0.95 and negative with probability 0.05, and a nonuser will test negative with probability 0.95 and positive with probability 0.05. develop a probability tree diagram to determine the posterior probability of each of the following outcomes of testing an athlete.

(a) the athlete is a drug user, given that the test is positive.

(b) the athlete is not a drug user, given that the test is positive.

(c) the athlete is a drug user, given that the test is negative.

(d) the athlete is not a drug user, given that the test is negative.

(e) use the corresponding excel template to check your answers in the preceding parts.

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

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

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

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

P ( D / - ) = 171 / 172

answer: it is 1: 47 pm

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: