Magnetic tape is slit into half-inch widths that are wound into cartridges. A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day for sharpness. If any dull blade is found, the assembly is replaced with a newly sharpened set of blades.
(a) If 10 of the blades in an assembly are dull, what is the probability that the assembly is replaced the first day it is evaluated?
(b) If 10 of the blades in an assembly are dull, what is the probability that the assembly is not replaced until the third day of evaluation? [Hint: Assume the daily decisions are independent, and use the geometric distribution.]
(c) Suppose on the first day of evaluation, two of the blades are dull, on the second day of evaluation six are dull, and on the third day of evaluation, ten are dull. What is the probability that the assembly is not replaced until the third day of evaluation? [Hint: Assume the daily decisions are independent. However, the probability of replacement changes every day.]