According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate. A system administrator wishes to see if the same percentages hold true for the e-mail traffic on her servers. She randomly selects e-mail messages and checks to see whether or not each one is legitimate. (Unless otherwise specified, round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 12.34%).
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.
According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate. A system administrator wishes to see if the same percentages hold true for the e-mail traffic on her servers. She randomly selects e-mail messages and checks to see whether or not each one is legitimate. (Unless otherwise specified, round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 12.34%).
a) Assuming that 90% of the messages on these servers are also spam, compute the
b) Compute the probability that the first legitimate e-mail she finds is the third or fourth message she checks.
c) Compute the probability that the first legitimate e-mail she finds is among the first three messages she checks.
d) On average, how many messages should she expect to check before she finds a legitimate e-mail? (Round your answer to one decimal place.)
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