Sorry I didn't responded earlier, I have been on the road and out of touch for a while.

First, this is one of those dumb questions, which I really hate, that the certification committees develop to confuse people. The answer usually lies in understanding the intent of the arcane question. Never the less we will forge ahead. Second, IMHO our esteemed colleague Mr. Scott has hit the nail on the head as usual. As he stated, I believe there is an error in the question.

By definition in the problem, the probability of defect A does NOT preclude the probability of defect B, therefore the events are not mutually exclusive. Given they are not mutually exclusive then the probability of independent event A or independent event B or both is the probability of A plus the probability of B minus the probablity of both:

P(A or B or both) = P(A) + P(B) - P(both)

Example, what is the probability of obtaining a jack or a diamond on one draw from a deck of cards. The probability of a jack is 4/52 = 0.077. The probability of diamond is 13/52 = 0.327. The probability of the jack of diamonds is 1/52 = 0.019. Therefore the answer is 0.077 + 0.327 - 0.019 = 0.308.

So, in the case in point the probability of both occurring is the probability of A, 0.83, multiplied by the probability of B, 0.83, which equals 0.6889. The probability of A or B or both is 0.83 plus 0.83 minus 0.6889 which is 0.9711.

If the probability of defect A or B or both is 0.9711 then the probability of no defect is 1.0000 - 0.9711 = 0.0289 or 0.029.

However, if we accept the probabilities given in the question (0.83 - 0.83 + 0.83 = 0.83) then the probability of no defects is 1.00 - 0.83 = 0.17 and as Mr. Scott states, the answer of 0.029 is the probability of no defects in two consecutive samples.

Regards,

Rick