Your colleague at Sun suggests that, since the yield is so poor, it might make sense to sell two sets of chips, one with 8 working processors and one with 6 working processors. We will solve this exercise by viewing the yield as a probability of no defects occurring in a certain area given the defect rate. For the Niagara, calculate probabilities based on each Niagara core separatel1y (this may not be entirely accurate, since the yield equation is based on empirical evidence rather than a mathematical calculation relating the probabilities of finding errors in different portions of the chip).
a. Using the yield equation for the defect rate above, what is the probability that a defect will occur on a single Niagara core (assuming the chip is divided evenly between the cores) in an 8-core chip?
b. What is the probability that a defect will occur on one or two cores (but not more than that)?
c. What is the probability that a defect will occur on none of the cores?
d. Given your answers to parts (b) and (c), what is the number of 6- core chips you will sell for every 8-core chip?
e. If you sell your 8-core chips for $150 each, the 6-core chips for $100 each, the cost per die sold is $80, your research and development budget was $200 million, and testing itself costs $1.50 per chip, how many processors would you need to sell in order to recoup costs?