A factory has three machines M1, M2, and M3 producing a large number of computer chips. Of the total daily production of items, 50% is produced on M1, 20% on M2, and 30% on M3. Records show that 4% of chips produced on M1 are defective, 2% produced of chips produced on M2 are defective and 2.5% of c
A factory has three machines M1, M2, and M3 producing a large number of computer chips. Of the total daily production of items, 50% is produced on M1, 20% on M2, and 30% on M3. Records show that 4% of chips produced on M1 are defective, 2% produced of chips produced on M2 are defective and 2.5% of chips produced on M3 are defective. The occurrence of a defective chip is independent of all other chips. One chip is chosen at random from a day's total production. (i) Show that the probability of being defective is 0.0315 (ii) Given that it is defective, find the probability that was produced on machine M1. [5]
Machine Production Share Defective Rate ------------------------------------------ M1 $P(M1) = 0.50$ $P(DM1) = 0.04$ M2 $P(M2) = 0.20$ $P(DM2) = 0.02$ M3 $P(M3) = 0.30$ $P(DM3) = 0.025$ Let $D$ = event that a randomly chosen chip is defective. --- By the Total Probability Theorem: $$P(D) = P(M1)P...