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