1)A factory runs three shifts. In a given day, 1% of the items produced by the first shift are defective, 2% of the second shift's item are defective, and 5% of the third shift's items are defective.

a.If the shifts all have the same productivity, what percentage of the items produced in a day are defective?

b.If an item is defective, what is the probability that it was produced by the third shift assuming all shifts have the same productivity?

c.If the productivities in the three shifts are 45% (first shift), 30% (second shift) and 25% (third shift), what is the probability that a defective item was produced by the first shift?