In October 1994, a flaw in a certain Pentium chip installed in computers was dis

Question

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?

Explanation / Answer

Probability of a flaw in any division= P(F)= 1/ 9 billion= 1/(9*109)

Probability of having no flaw in a division= P(FI)= 1-P(F)= 1- (1/(9*109))

By binomial theorem, probability of having no errors for n divisions =(1-P(F))n

Hence Probability of having no errors in 1 billion divisions= (1- (1/9*109))10^9

Probability of at least 1 error in 1 billion division chips= 1- No errors in 1 billion divisions

= 1- (1-P(F))n

= 1- (1-(1/9*109))10^9

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