Given the following drug screening results for marijuana: Out of 600 positive te
ID: 3266731 • Letter: G
Question
Given the following drug screening results for marijuana: Out of 600 positive test results, only 100 were true positive, and out of 10 00 negative test results, only 6 5 were false negative.
a. Construct a table to represent the results. See Table 4 - 1 from Example 2 on page 170 in section 4.5 for an example of such table.
b. Find the probability that when one subject is randomly selected, the subject tested positive or negative.
c. Find the probability that when one subject is randomly selected, the subject tested true positive or false negative.
d. Find the probability that when one subject is randomly selected, the subject tested true positive and false negative.
e. Find the probability that when one subject is randomly selected, the subject tested positive given that the subject uses drugs.
f. Find the probability that when one subject is randomly selected, the subject uses drugs given that the subject tested positive.
g. Are the probability values from part e. and part f. equal?
h. Find the probability that when two subjec ts are randomly selected with replacement that the first subject tests true positive and the second subject tests false negative.
i. Find the probability that when two subjects are randomly selected with replacement th at the first subject tests positive given that the subject uses drugs, and the second subject tests negative given that the subject uses drugs.
Explanation / Answer
From the given data,
(a)
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(b)Probability that subject tested positive or negative is = 600/1600 + 1000/1600 (as the two events are mutually exclusive) = 1
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(c)probability that subject tested true positive or false negative = 100/1600 + 935/1600 = 0.65
(two events are m.e.)
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(d)probability that subject tested is TP and FN = 0 (as the intersection of two mutually exclusive event is 0 ! )
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(e)probability(subject tested positive | subject uses drugs)
=P[ TP | (TP+FN) ]
=100/1035
=0.097
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(f)Probability(subject uses drug | tested positive)
=P[ TP | TP+FP ]
=100/600
=0.17
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(g) Check yourself !
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(h)when two subjects are randomly selected with replacement then they will be two independent event.
So, Prob[1st subject tests TP and 2nd subject tests FN]
= P[subject tested TP] * P[subject tested FN]
=100/1600 * 935/1600
=0.037
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(i) Sly,
Prob[1st tests positive|uses drug and 2nd tests negative|uses drug]
=P[tests positive | uses drug] * P[tests negative|uses drug]
=100/1035 * 935/1035
=0.087
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Observed Presence Observed Absence Predicted Presence True Positive(TP) False Positive(FP) Predicted Absence False Negative(FN) True Negative(TN)Related Questions
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