Question

71.

Use the table below to find the probability.

	Positive Test Result	Negative Test Result
Subject Uses Drugs	44 (True Positive)	6 (False Negative)
Subject is Not a Drug User	90 (False Positive)	860 (True Negative)

A. If 2 of the 1000 test subjects are randomly selected, find the probability that both had false positive results. Assume that the 2 selections are made without replacement. (Round to 4 decimals)

B.

If 3 of the 1000 test subjects are randomly selected, find the probability that all had false negative results. Assume that the 3 selections are made with replacement. (Round to 9 decimals)

74.

Determine whether a probability distribution is given. If a probability distribution is given, find its mean. (Round to the nearest thousandth). If a probability distribution is not given, state (not a probability distribution). (Check your spelling!)

x	P(x)
0	0.658
1	0.287
2	0.050
3	0.004
4	0.001

Answer 1

71.  

	Positive Test Result	Negative Test Result	Total
Subject Uses Drugs	44	6	50
Subject is not a Drug User	90	860	950
Total	134	866	1000

A. There are total 1000 subjects and 90 "False Positive" Subjects.
So 2 subjects can be chosen from 1000 subjects in- ways. (by without replacement)
and 2 subjects can be chosen from 90 "False Positive" subjects in - ways (by without replacement)

The Probability that if 2 subjects are randomly chosen from 1000 subjects. Then the probability that both had false positive results is:

B. There are total 1000 subjects and 6 "False Negative" Subjects.

So 3 subjects can be chosen from 1000 subjects in- ways. (by with replacement)
and 3 subjects can be chosen from 6 "False negative" subjects in  - ways (by with replacement)

The Probability that if 3 subjects are randomly chosen from 1000 subjects. Then the probability that all had false negative cases is:

74. Determination whether the following the given probability distribution or not:
The given distribution is:

x	p(x)
0	0.658
1	0.287
2	0.050
3	0.004
4	0.001

To determine whether this distribution is probability distribution or not we've to check whether-

1. for all i=0,1,2,3,4
2. 

So as we can see that here all are between 0 to 1, so first condition satisfied.
and

We can say that the given distribution is probability distribution.

Mean=E(X)=
=0.403

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