Suppose that a flaw in a certain computer chip installed in computers was discov

Question

Suppose that a flaw in a certain computer 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 12 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 12 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? (Round your answer to four decimal places.)

Explanation / Answer

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes = n p = (1,000,000,000) / (1/ 12,000,000,000) =   0.083333333      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.920044415

Thus, P(at least 1) = 1 - P(0) = 0.079955585 = 0.0800 [ANSWER]

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