Answer: 0.4169
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