Agroup of asu sustainability students took 200 water samples from groundwater in different places in the phoenix valley. they test those samples for a certain chemical. the test is not 100% correct. if the sample contains the chemical, the test shows a positive test results 97% of the time. if the sample does not contain the chemical, it give a negative result 89% of the time. if 15 groundwater samples contain chemicals, what is the probability the sample contains a chemical if you have a positive test return for the sample?

 0.4169

Step-by-step explanation:

Given :  If the sample contains the chemical, the probability that test shows a positive test results = 0.97

If the sample does not contain the chemical, then the probability that it give a negative result =0.89

Then, If the sample does not contain the chemical, the probability that test shows a positive test results =1-0.89=0.11

Out of 15 , number of samples contains chemical shows positive results=

No. of sample does not contain chemical = 200-15=185

Out of 185 , number of samples does not contains chemical shows positive results =

Sample have positive test = 14.55+20.35= 34.90

Now, the probability the sample contains a chemical if you have a positive test return for the sample :-

Hence, the  probability the sample contains a chemical if you have a positive test return for the sample =0.4169

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

c) yes, because of asa or aas