Question

Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested a) What is the probability that the first non-defective engine will be found on the second trial? b) What is the probability that the third non-defective engine will be found i. on the fifth trial? ii. on or before the fifth trial? c. Find the mean and variance of the number(position) of the trial on which: i. the first non-defective engine is found. ii. the third non-defective engine is found. d. Given that the first two engines tested were defective, what is the probability that at least two more engines must be tested before the first non-defective is found? e. Find the probability that out of 8 randomly selected engines exactly 5 will be defective.