Suppose that a new Internet company Mumble .com requires all employees to take a drug test. Mumble .com can afford only the inexpensive drug test—the one with a 5% false-positive rate and a 10% false-negative rate. (That means that 5% of those who are not using drugs will incorrectly test positive and that 10% of those who are actually using drugs will test negative.) Suppose that 10% of those who work for Mumble.com are using the drugs for which Mumble is checking. (Hint: It may be helpful to draw a tree diagram to answer the questions that follow.) a. If one employee is chosen at random, what is the probability that the employee both uses drugs and tests positive? b. If one employee is chosen at random, what is the probability that the employee does not use drugs but tests positive anyway? c. If one employee is chosen at random, what is the probability that the employee tests positive? d. If we know that a randomly chosen employee has tested positive, what is the probability that he or she uses drugs?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose that a new Internet company Mumble
.com requires all employees to take a drug test. Mumble
.com can afford only the inexpensive drug test—the one
with a 5% false-positive rate and a 10% false-negative
rate. (That means that 5% of those who are not using
drugs will incorrectly test positive and that 10% of those
who are actually using drugs will test negative.) Suppose
that 10% of those who work for Mumble.com are using
the drugs for which Mumble is checking. (Hint: It may
be helpful to draw a tree diagram to answer the questions
that follow.)
a. If one employee is chosen at random, what is the
probability that the employee both uses drugs and tests
positive?
b. If one employee is chosen at random, what is the
probability that the employee does not use drugs but
tests positive anyway?
c. If one employee is chosen at random, what is the probability that the employee tests positive?
d. If we know that a randomly chosen employee has tested
positive, what is the probability that he or she uses
drugs?
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