20. The quadratic equation $2x^2 - \sqrt{5}x + 1 = 0$ has * two distinct real roots no real roots two equal real roots more than 2 real r
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A first step towards identifying spam is to create a list of words that are more likely to appear in spam than in normal messages. For instance, words like buy or the brand name of an enhancement drug are more likely to occur in spam messages than in normal messages. Suppose a specified list of words is available and that your data base of 4000 messages contains 1700 that are spam. Among the spam messages, 1000 contain words in the list. Of the 2300 normal messages, only 297 contain words in the list. Obtain the probability that a message is spam given that the message contains words in the list.
Sri K.
BE FAST PLEASE TELL OP OPOPOP
Sahil K.
Definitions of e-mail spam, or junk e-mail, typically include the idea that the e-mail is unsolicited and sent in bulk. Beginning in the early 1990 s the amount of email spam grew steadily until recently, with a total volume of over 100 billion e-mails per day in April $2008 .$ The amount being received has begun to decrease due to the use of better filtering software. As unbelievable as it might be, fewer than 200 spammers send about $80 \%$ of all spam. The chart below lists the percentage of e-mail spam relayed by each country in 2007. \begin{array}{lc} \text { Country } & \text { Percentage } \\ \hline \text { Brazil } & 4.1 \\ \text { China } & 8.4 \\ \text { EU } & 17.9 \\ \text { France } & 3.3 \\ \text { Germany } & 4.2 \\ \text { India } & 2.5 \\ \text { Italy } & 2.8 \\ \text { Poland } & 4.8 \\ \text { Russia } & 3.1 \\ \text { S Korea } & 6.5 \\ \text { Turkey } & 2.9 \\ \text { UK } & 2.8 \\ \text { US } & 19.6 \\ \hline \end{array} a. Construct a bar graph of this information with the percentages in declining order. b. Explain why a Pareto diagram of this information cannot be constructed.
Descriptive Analysis and Presentation of Single-Variable Data
Graphs, Pareto Diagrams, and Stemandleaf Displays
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