Three factories A ,   B and C produce the same product. The factory A produces twice as many as B produces while the factories B and C produce in the same quantity. It is known that 2 % of the products of A as well as C   are defective while 4 % of the products of B are defective. All the products of the three factories are stocked together. If a product is selected at random from the stock, what is the pro

Step-by-step solution

Let A ,   B   and C produce 2 n ,   n   and n products. Let E 1 = event of a product being produced at A E 2 = event of a product being produced at B E 3 = event of a product being produced at C . ∴  P E 1 = 2 n 2 n + n + n = 1 2 P E 2 = n 2 n + n + n = 1 4 P E 3 = 1 4 . Also, probability of a product being defective when produced at A = 2 1 0 0 = 1 5 0 , Similarly, P D / E 2 = 4 1 0 0 = 1 2 5   P D / E 3 = 2 1 0 0 = 1 5 0 , The probability that the product is defective =