Question

Use the following results from a test for marijuana​ use, which is provided by a certain drug testing company. Among 141 subjects with positive test​ results, there are 25 false positive results. Among 153 negative​ results, there are 3 false negative results

a. How many subjects were included in the​ study?

b. How many subjects did not use​ marijuana?

c. What is the probability that a randomly selected subject did not use​ marijuana?

Winning the jackpot in a particular lottery requires that you select the correct

four numbers between 1 and 47 ​and, in a separate​ drawing, you must also select the correct single number between 1 and

22. Find the probability of winning the jackpot.

Answer 1

a)

Among the 141 subjects with positive test results, there are 25 false positive results.

Among the 153 negative results, there are 3 false negative results.

So total 141 + 153 = 294 subjects were included in the study.

b) 153 are negative results, 25 are false positive results and 3 false negatives.

So 153 + 25 - 3 = 175 subjects did not use marijuana.

c) Total subjects are 294 and subjects did not use marijuana are 175.

So the probability that a randomly selected subject did not use marijuana = 175 / 294 = 0.5952

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Winning the jackpot in a particular lottery requires that you select the correct four numbers between 1 and 47.

First, find the possible combinations of 4 balls out of 47:

47C4 = 47! / (4! * 43!) = 178365

Multiply this by the possible combinations of 1 ball out of 22 = 22

22*178365 = 3924030

So the probability of winning the jackpot is 1 / 3924030.