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

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step-by-step explanation: