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? A. 0 B. 0.09 C. 0.11 D. 0.44

Answer 1

Answer:The correct answer is option A.

Step-by-step explanation:

We have been given that

Probability that the land has oil =
`P_o`= 45% = 0.45

Accuracy rate of the kit indicating the oil in the soil =
`P_(k,o)`= 80 %= 0.80

Rate of the kit indicating no oil in the soil =
`P_(k,n)` 1 - 0.8 = 0.2

Probability of the land has oil and test kit predicts that there is no oil:(And means multiplication, so we will multiply the above two probabilities)

`P_o* P_(k,n)=0.45* 0.2=0.09`

Hence, the probability that the land has oil and the test predicts that there is no oil is 0.09.

Answer 2

B. 0.09

Step-by-step explanation:

Probability that the land has oil = 45%

= 0.45 (converted into decimal)

Probability of accuracy of the kit = 80%

= 0.80 (converted into decimal)

Probability that the kit detects no oil = Total probability - Probability of accuracy of the kit

= 1 - 0.80 [total probability of any event is always 1]

= 0.20

Probability that the land has oil and the test predicts that there is no oil = Probability that the land has oil x Probability that the kit detects no oil

= 0.45 x 0.20

= 0.09