Three machines X,Y,Z are produced respectively 50%,30%,and 20% of the total number of items in a factory.The output of these machines are 3%,4% and 5% respectively.If an item is selected at random,find
1)The probability that the item is defective,
2)Probability that the item is produced by machine X,machine Y,machine Z?

1. Find each probability of:
i. Item is from X and is defective.
ii. Item is from Y and is defective.
iii. Item is from Z and is defective.

Add them up.

2. Divide the probability of I by the total you got in 1. to get the probability that it came from X. Do the same for the others.