Question

Stainless steel bolts used in boat construction are checked as they are manufactured. 90% of these pass this check. Of those that fail this check, 30% are seriously flawed and must be discarded. The remainder undergo an additional correction process, and 80% of the bolts which have gone through the correction process pass the second check. Any that fail this second check are discarded. (a) What is the probability that a randomly selected bolt of this type will eventually pass a check? In your working, define relevant events. [6 marks) (b) Given that a bolt of this type passed a check, what is the probability that it passed the first check? (3 marks

Answer 1

solution: - ܀ P: Pass check one P2 : pass check two D: Discarded PICC) = 0.3 P/P = 0.9 P(P2) 0.8 a) P(P2) = P1 P20 P;) + P1 P2 apg ples - 7 P2 PIP) PIPO Pic 0.8 x0.9 + (1 -0.3) X 0.1 PL = 0.727 b) Ple PI POP2) 0.8xo.9 0.990 P(P2) 0.727