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.

  1. Show that the probability of being defective is 0.0315
  2. Given that it is defective, find the probability that was produced on machine M1.

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