Question

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 that there is no oil?

Answer 1

Probability is normally written in fractin form (can also be written in percent but not as common)
it is 45% that the land has oil
 44%=44/100=11/25
but the sensor is 80% acurate
 80%=80/100=8/10=4/5
so we multilly the 2 things
 11/25 times 4/5=44/125
divide to find percent 44/125=0.352
round to 0.35
0.35/1=3.5/10=35/100=7/20
probability is 7/20

Answer 2

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% --> $\frac{45}{100}$

$\frac{45}{100}--\ \textgreater \ \frac{3*3*5}{2*2*5*5}$

$\frac{3*3*5}{2*2*5*5}--\ \textgreater \ \frac{3*3}{2*2*5}$

$\frac{3*3}{2*2*5}--\ \textgreater \ \frac{9}{20}$

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% --> $\frac{20}{100}$

$\frac{20}{100}--\ \textgreater \ \frac{2}{10}$

$\frac{2}{10}--\ \textgreater \ \frac{1}{5}$

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.

$\frac{9}{20}*\frac{1}{5}$

$\frac{9}{20*5}$

$\frac{9}{100}$

So the probability of there BEING oil and the kit predicting NO oil is 9 in 100 chances.