Question

A company delivers solar cells to countries G, K and S. 50% of the cells are delivered to country G, 25% to K and the remaining to S. From experience the company knows that country G returns 1% of the delivered cells, country G returns 2% and country K returns 4%. What is the probability that a randomly chosen solar cell is returned?

Answer 1

Let events G, K and S show that cell is delivered in country G, K and S respectively.

Let R shows the event that country returned delivered cell.

From the given information we have

P(G) = 0.50, P(K) = 0.25, P(S) = 1 - 0.50 -0.25 = 0.25

And

P(R|G) = 0.01, P(R|K) = 0.04, P(R|S) = 0.02

By the laws of total probability, the probability that a randomly chosen solar cell is returned is

P(R) = P(R|G)P(G) + P(R|S)P(S)+ P(R|K)P(K) = 0.01 * 0.50 + 0.02 * 0.25 + 0.04 *0.25 = 0.02