3, Suppose 1,000 athletes are lested for pot. One in 5 uses pot. The test has a

Question

3, Suppose 1,000 athletes are lested for pot. One in 5 uses pot. The test has a 2% false positive rate and a 1% false negative rate. If an athlete tests positive, what is the probability that the athlete is a mon-user? 4. A bag contains 8 red, 4 white, and 8 blue marbles b) find the probability of drawing first a red then a blue marble if the red marble is no replaced 5. A die is rolled twice a) What is the probability of rolling a 2 then a number greater than 4? b) What is the probability of the first roll being a 5 or the second roll being a 1

Explanation / Answer

Ans:

1)

P(user)=1/5=0.2

P(non user)=1-0.2=0.8

P(positive/non user)=0.02

P(negative/user)=0.01

P(positive/user)=1-0.01=0.99

P(positive)=P(positive/user)*P(user)+P(positive/non user)*P(non user)

=0.99*0.2+0.02*0.8

=0.214

P(non user/positive)=P(positive/non user)*P(non user)/P(positive)

=0.02*0.8/0.214

=0.075

2)

a)P(white or blue)=(4+8)/20=12/20=6/10=0.6

b)P(first red the blue)=(8/20)*(8/19)=64/380=0.1684

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