In: Statistics and Probability
3. Probability
An accident at Eagle Aspirin Company led to bottles of their
aspirin pain reliever being incorrectly manufactured. The 50 tablet
bottles of aspirin were each given 45 pain reliever tablets and 5
placebo tablets by mistake. Suppose you have purchased a faulty
bottle of Eagle aspirin pain reliever containing 50 tablets. You
randomly select three tablets from the bottle to relieve your
headache from studying statistics.
a.
What is the probability that all three tablets you selected are
pain reliever tablets?
b.
What is the probability that all three tablets you selected are
placebo tablets?
c.
What is the probability that exactly one of the three tablets you
selected is a pain reliever tablet?
d.
What is the probability that at least one of the three tablets you
selected is a pain reliever tablet?
a) Probability that all 3 are pain reliever tablets
= Number of ways to select 3 pain reliever tablets from 45 pain reliever tablets / Total ways to select 3 tablets from 50 tablets
Therefore 0.7240 is the required probability here.
b) Probability that all 3 are placebo is computed in similar way as above part as:
Therefore 0.0005 is the required probability here.
c) Probability that exactly one of them is a pain reliever tablet
= Number of ways to select 1 pain reliever from 45 pain relievers * Number of ways to select 2 placebo from 5 placebos / Number of ways to select 3 tablets from 50 tablets
Therefore 0.0230 is the required probability here.
d) Probability that at least one of the three tablets selected is a pain reliever tablet is computed here as:
= 1 - Probability that none of them are pain reliever tablets
= 1 - 0.0005
= 0.9995
Therefore 0.9995 is the required probability here.