The manufacturer of a price-reading optical scanner claims that the probability it will misread the price of any product by misreading the “bar code” on a product’s label is .001. At the time one of the scanners was installed in a supermarket, the store manager tested its performance. Let Y be the number of trials (i.e., the number of prices read by the scanner) until the first misread price is observed.

a. If the manufacturer’s claim is correct, find the probability distribution for Y. (Assume the trials represent independent events.)

b. If the manufacturer’s claim is correct, what is the probability that the scanner will not misread a price until after the fifth price is read?

c. If in fact the third price is misread, what inference would you make about the manufacturer’s claim? Explain.