An electronic company produces a particular cell phone at tw

An electronic company produces a particular cell phone at two different plants 1 and 2. 100% of the cell phone from plant 1 and 100% of the cell phone from plant 2 are defective (0 < < 1 and 0 < < 1). Plant 1 produces twice as many cell phones as plant 2 each week.

(a) What is the probability that a cell phone, randomly chosen from a week’s production, is not defective?

(b) If the chosen cell phone is defective, what is the probability that it came from plant 1?

(c) A new process for the production of cell phones is invented and both plants install extra production line using it. The new process is cheaper but produces fewer reliable(non-defective) cellphones, only 75% of items produced in this new way being reliable(non-defective). Plant 1 fails to implement its new production line efficiently, and only 100% of its output is made in this manner. Plant 2 does better: it produces 100% of its output by the new process, and now produces twice as many cell phones in all as plant 1 (0 < < 1 and 0 < < 1). What is the probability that a cell phone, randomly chosen from a week’s production, is defective?

Solution