Jason inherited a piece of land from his great uncle. owners in this 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. if the test predicts that there is no oil, what is the probability after the test that the land has oil?
a)0.1698
b)0.2217
c)0.5532
d)0.7660
its not c

answer: our probability after the test that the land has oil = 0.234.

step-by-step explanation:

since we have given that

probability that the land has oil = 45%

probability that the land has no oil is given by

probability that the accuracy rate of indicating oil in the soil = 80%

probability that the test is not accurate is given by

we need to find that probability after the test that the land has oil :

as we know the formula of " bayes theorem " :

[tex]p(l/o)=0.45\ and\ p(l/not o)=0.55p(o)=0.80\ and\ p(not\ oil)=0.20p(not\ o\mid l)=\frac{p(not\ o).p(\l\mid not\ o)}{p(o).p(l\mid not\ o)+p(o).p(l\mid o)}p(not\ o\mid l)=\frac{0.20\times 0.55}{0.20\times 0.55+0.8\times 0.45}p(not\ o\mid l)=\frac{0.11}{0.11+0.6}=\frac{0.11}{0.47}=0.234/tex]

hence, our probability after the test that the land has oil = 0.234.

Since it is stated that the machine he bought only predict about 80%. thus, about 20% are still possible that there are oils in the land that he owned.
in a 100% value = 80% were the 0 possibillites detected by the machine and 20% are still the possibility that it has an oil.
=> 80% = 0.80
=> 20% = 0.20
in the given choices. letter b has the closest value to the 20% that we expected.
thus, let's have b as an answer.

(answer 2 )i’m very smart that’s how i know the answer.

Horizontal change or the change of x