Select the correct answer.Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has oil and the test predicts it?A. 0.09B. 0.11C. 0.36D. 0.44Reset Next

Accepted Solution

Answer:Option A 0.1698Step-by-step explanation:Given that Jason has a chance for getting oil as 45%THe kit he buys show accurate result with 80% probabilityLet A1- Event that the land has oilA2 - Event that the land has no oilB- The test gives negative resultA1 and A2 are mutually exclusive and exhaustiveP(A1) = 0.45 and P(A2) =0.55Hence we can use Baye theoremThen P(B) = P(A1B)+P(A2B)=[tex]0.45(0.20)+0.55(0,80)\\=0.09+0.0.44\\=0.53[/tex]Reqd prob =P(A1/B) =[tex]\frac{P(A1B)}{P(B)}\\ =\frac{0.09}{0.53}\\\\=0.1698[/tex]