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anonymous
 one year ago
Jason inherited a piece of land from his greatuncle. 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 no oil and the test shows that it has oil?
Answer choices:
0.09
0.11
0.36
0.44
anonymous
 one year ago
Jason inherited a piece of land from his greatuncle. 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 no oil and the test shows that it has oil? Answer choices: 0.09 0.11 0.36 0.44

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know it's not A or C. But I tried the formula and got 1.778 but I don't know what to do from there.

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.0Let D be the event that oil is detected Let O be the probability that oil exists We are given that \(P(O)=0.45\) and \(P(DO)=0.8\) We also know that $$ P(DO)=\frac{P(D\cap O)}{P(O)} $$ Where \(\bar{O}\) is the event that there is no oil Then $$ P(D\cap O)=P(DO)P(O)=0.80\times0.45 $$ We also know that $$ P(DO)+P(D\bar{O})=1\\ \text{Which is the same as}\\ \frac{P(D\cap O)}{P(O)}+\frac{P(D\cap \bar{O})}{P(\bar{O})}=1\\ $$ We need \(P(D\cap \bar{O})\), the probability that oil is detected but none exists: $$ \frac{P(D\cap O)}{P(O)}+\frac{P(D\cap \bar{O})}{P(\bar{O})}=1\\ \implies P(D\cap \bar{O})=\left(1\frac{P(D\cap O)}{P(O)}\right )P(\bar{O})\\ =(10.8)0.55 $$ Does this make sense?
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