Answer:
The required probability is 0.6053
Step-by-step explanation:
Consider the provided information.
Among 148 subjects with positive test results, there are 28 false positive results.
That means the true positive results are: 148-28=120
Among 156 negative results, there are 4 false negative results.
That means the positive results are 156-4=152
Positive Negative Total
Use marijuana F negative 120 4 124
Not use marijuana F positive 28 152 180
Total 148 156 304
The probability that the subject tested negative or did not use marijuana.
P(Negative∪ not use marijuana)=[P(Negative)+P(Not use marijuana)-P(negative ∩ not use marijuana)]
P(Negative∪ not use marijuana) = ![\frac{156}{304} +\frac{180}{304} -\frac{152}{304}](https://tex.z-dn.net/?f=%5Cfrac%7B156%7D%7B304%7D%20%2B%5Cfrac%7B180%7D%7B304%7D%20-%5Cfrac%7B152%7D%7B304%7D)
P(Negative∪ not use marijuana) = ![\frac{156+180-152}{304}](https://tex.z-dn.net/?f=%5Cfrac%7B156%2B180-152%7D%7B304%7D)
P(Negative∪ not use marijuana) = ![\frac{184}{304}](https://tex.z-dn.net/?f=%5Cfrac%7B184%7D%7B304%7D)
P(Negative∪ not use marijuana) ≈ ![0.6053](https://tex.z-dn.net/?f=0.6053)
Hence, the required probability is 0.6053