A machine generates defectives from time to time in a random manner. the engineer for the machine notices that defectives seem to be grouping hence nonrandom, thereby suggesting a malfunction in some part of the machine. one test of nonrandomness is based on the number of runs or defectives and nondefectives. the smaller the number of runs, the greater the evidence of nonrandomness. of 12 components drawn, the first 10 were not defective and the last 2 were defective. assume randomness, what is the probability
a. of getting this arrangement, resulting in 2 runs, given that 10 of the 12 components are not defective?
b. of getting 2 runs
c. that the number of runs is less than or equal to 3?