So,
We are trying to find the compound probability of there BEING oil and the test predicting NO oil.
The percent chance of there actually being oil is 45%. We can convert this into fraction form and simplify it.
45% --> [tex] \frac{45}{100} [/tex]
[tex]\frac{45}{100}--\ \textgreater \ \frac{3*3*5}{2*2*5*5} [/tex]
[tex]\frac{3*3*5}{2*2*5*5}--\ \textgreater \ \frac{3*3}{2*2*5}[/tex]
[tex]\frac{3*3}{2*2*5}--\ \textgreater \ \frac{9}{20} [/tex]
That is the simplified fraction form.
The kit has an 80% accuracy rate. Since we are assuming that the land has oil, we need the probability that the kit predicts no oil.
The probability that the kit detects no oil will be the chance that the kit is not accurate, which is 20% (100 - 80 = 20). We can also convert this into fraction form and simplify it.
20% --> [tex] \frac{20}{100} [/tex]
[tex]\frac{20}{100}--\ \textgreater \ \frac{2}{10}[/tex]
[tex]\frac{2}{10}--\ \textgreater \ \frac{1}{5}[/tex]
That is the probability of the kit not being accurate (not predicting any oil).
To find the compound probability of there being oil and the kit not predicting any oil, we simply multiply both fractions together.
[tex]\frac{9}{20}*\frac{1}{5}[/tex]
[tex]\frac{9}{20*5}[/tex]
[tex]\frac{9}{100}[/tex]
So the probability of there BEING oil and the kit predicting NO oil is 9 in 100 chances.
