ENGM2032, Applied Probability and Statistics
Winter 2006
Assignment #3
Due:
Start of class, Tuesday, Jan 24, 2006
1) Assume that 70% of companies that maintain a website sell their products online. It is estimated that
80% of the companies that offer online sales of products experience at least one hacking attack on their
websites a day, whereas this number is only 15% for the companies that do not sell products online.
a) What is the probability that a randomly selected company that maintains a website experiences at
least one hacking attack a day?
b) If, on a certain day, a company experiences at least one hacking attack, what is the probability that
it sells its products online?
2) A software company has recently introduced a new program that allows the user to convert graphical
files representing text (e.g., a scanned journal article) into actual text files. Before the market release of
the product, an independent research company was contracted to analyze the reliability of the software,
i.e. to assess the probability of erroneous symbol recognition. Each symbol was analyzed separately.
For example, it was established that, on average, out of 1000 letters ‘a’ in the graphical file, 60 are
recognized as other symbols. It was also found that out of 1000 symbols that are anything but letter ‘a’,
47 are recognized as letter ‘a’. It is known that out of 1000 letters in a modern English text, on average,
86 letters are ‘a’ (as opposed to 114 letters ‘e’, the most frequently used letter of the alphabet).
a) What is the probability that a randomly selected symbol is recognized by the software as a letter
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