Respuesta :
Answer: The probability after the test that the land has oil is 0.09.
Explanation:
Let A is the event that the land has oil.
It is given that there is a 45% chance that the land has oil. So,
[tex]P(A)=\frac{45}{100}[/tex]
The probability that the land has no oil is,
[tex]P(A)=[tex]P(A')=1-P(A)=1-\frac{45}{100}=\frac{100-45}{100}=\frac{55}{100}[/tex]
Let B is the event that the kit gives the accurate rate of indicating oil in the soil. So,
[tex]P(B)=\frac{80}{100}[/tex]
The probability that the kit gives the false result is,
[tex]P(B')=1-P(B)=1-\frac{80}{100}=\frac{100-80}{100}=\frac{20}{100}[/tex]
Events A and B are two independent events and we have to find the probability that the last has oil and kit given false result.
[tex]P(A\cap B')=P(A)P(B')[/tex]
[tex]P(A\cap B')=(\frac{45}{100})(\frac{20}{100})=\frac{900}{10000} =\frac{9}{100}=0.09[/tex]
Therefore, the if the test predicts that there is no oil, then the probability after the test that the land has oil is 0.09.
