In an article that appears on a website,† Carlton Gunn, a public defender in Seattle, Washington, wrote about how he uses statistics in his work as an attorney. He states the following.I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a "dirty" (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given—say 99 in 100—are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false.Define the following events as given below.TD = event that the test result is dirtyTC = event that the test result is cleanD = event that the person tested is actually dirtyC = event that the person tested is actually clean(a)Using the information in the quote, compute the following values.(i)P(TD|D) (ii)P(TD|C) (iii)P(C) (iv)P(D) (b)Use the probabilities from part (a) to construct a hypothetical 1,000 table. (Round your answers to the nearest integer.) TDTCTotalD C Total 1,000(c)What is the value of P(TD) based on the table values? (d)Use the information in the table to calculate the probability that a person is clean given that the test result is dirty, P(C|TD). Is this value consistent with the argument given in the quote? Explain.Yes, this value is consistent with the argument given in the quote, namely, half of the dirty tests are false.No, this value is not consistent with the argument given in the quote, namely, half of the dirty tests are false.

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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.2: Introduction To Probability

Problem 52E

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In an article that appears on a website,† Carlton Gunn, a public defender in Seattle, Washington, wrote about how he uses statistics in his work as an attorney. He states the following.

I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a "dirty" (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given—say 99 in 100—are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false.

Define the following events as given below.

TD = event that the test result is dirty
TC = event that the test result is clean
D = event that the person tested is actually dirty
C = event that the person tested is actually clean

(a)

Using the information in the quote, compute the following values.

(i)

P(TD|D)

(ii)

P(TD|C)

(iii)

P(C)

(iv)

P(D)

(b)

Use the probabilities from part (a) to construct a hypothetical 1,000 table. (Round your answers to the nearest integer.)

	TD	TC	Total
D
C
Total			1,000

(c)

What is the value of

P(TD)

based on the table values?

(d)

Use the information in the table to calculate the probability that a person is clean given that the test result is dirty,

P(C|TD).

Is this value consistent with the argument given in the quote? Explain.

Yes, this value is consistent with the argument given in the quote, namely, half of the dirty tests are false.No, this value is not consistent with the argument given in the quote, namely, half of the dirty tests are false.

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