Question

what does the "The probability of a correct inference:" means in this question and how can i solve it

Answer 1

1. The probability that the test-taker doesn't use drugs is 0.4311.

2. The probability of a false negative is 0.0222.

3. The probability of a correct inference is 0.9667.

Part 1.

Based on the contigency table shown above, the probability that the test-taker doesn't use drugs can be calculated by dividing the total number of test-takers by the number of people who doesn't use drugs as follows;

P(doesn't use drugs) = 194/450

P(doesn't use drugs) = 0.4311.

Part 2.

Based on the contigency table shown above, the probability of a false negative can be calculated by dividing the number of people who use drugs (negative) by the total number of test-takers as follows;

P(false negative) = 10/450

P(false negative) = 0.0222.

Part 3.

Based on the contigency table shown above, the probability of a false negative can be calculated by adding the number of people who doesn't use drugs (negative) and those who use drugs (positive), and then dividing by the total number of test-takers as follows;

P(correct inference) = (189 + 246)/450

P(correct inference) = 435/450

P(correct inference) = 0.9667.

Answer 2

The probability that the test-taker doesn't use drugs is the ratio of the number of people who take drugs to the total number of people. Hence the probability that the test-taker doesn't take drug is

= 194/450

= 0.4311

2.