Question

A machine for producing a new experimental electronic component generates defectives from time to time in a random manner. The supervising engineer for a particular machine has noticed that defectives seem to be grouping (hence appearing in a nonrandom manner), thereby suggesting a malfunction in some part of the machine. One test for non-randomness is based on the number of runs of defectives and non-defectives (a run is an unbroken sequence of either defectives or nondefectives). The smaller the number of runs, the greater will be the amount of evidence indicating non-randomness. Of 12 components drawn from the machine, the first 10 were not defective, and the last 2 were defective (NNNNNNNNNNDD). Assume randomness. What is the probability of observing

a) This arrangement (resulting in two runs) given that 10 of the 12 components are not defective?

b) Two runs?

Answer 1

SOLUTION:-