In: Statistics and Probability
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.
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.