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

B. 0.09

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

The correct answer is option A.

Explanation:

We have been given that

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

Accuracy rate of the kit indicating the oil in the soil == 80 %= 0.80

Rate of the kit indicating no oil in the soil = 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)

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