When circuit boards employed in the manufacture of portable disk drives are tested, the long-run percentage of defectives is 5%. Assume that the events that the boards are defective or not occur independently of each other.
a) Calculate the probability of finding exactly 3 defective circuit boards in a batch of twenty five.
b) Calculate the probability of finding at most 3 defective circuit boards in a batch of twenty five.
c) Calculate the probability of finding more than 1 but less than 4 defective circuit boards in a batch of twenty five.
d) Calculate the probability that at least 5 circuit boards have to be tested before a defective circuit board is found.