In October, 1994, a flaw in a certain Pentium chipinstalled in computers was discovered that could result ina wrong answer when performing a division. The manufacturerinitially claimed that the chance of any particulardivision being incorrect was only 1 in 9 billion, so that itwould take thousands of years before a typical userencountered a mistake. However, statisticians are nottypical users; some modern statistical techniques are socomputationally intensive that a billion divisions over ashort time period is not outside the realm of possibility.Assuming that the 1 in 9 billion figure is correct and thatresults of different divisions are independent of oneanother, what is the probability that at least one erroroccurs in one billion divisions with this chip?
In October, 1994, a flaw in a certain Pentium chip
installed in computers was discovered that could result in
a wrong answer when performing a division. The manufacturer
initially claimed that the chance of any particular
division being incorrect was only 1 in 9 billion, so that it
would take thousands of years before a typical user
encountered a mistake. However, statisticians are not
typical users; some modern statistical techniques are so
computationally intensive that a billion divisions over a
short time period is not outside the realm of possibility.
Assuming that the 1 in 9 billion figure is correct and that
results of different divisions are independent of one
another, what is the probability that at least one error
occurs in one billion divisions with this chip?
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