Thread: How to do this problem

How to start for this problem?


Three machines X, y, Z with capacities proportional to 2: 3 : 4 are producing bullets. The probability that the machines produce defective bullets are 0.1, 0.2 and 0.1 respectively. A bullet is taken from a day's production and found to be defective.What is the probability that it came from machine X ? Identify the most likely machine that has produced it.

(1) Find the defective products proportionality: (2*0.1) : (3*0.2) : (4*0.1) --> 0.2 : 0.6 : 0.4
(2) Now you know that the most probable machine is Y, 50% of all defective products are produced by Y.
(3) The probability that X produced the given defective bullet is 0.2/(0.2+0.6+0.4)=1/6