A manufacturer knows that its senior welders will produce defective items 1 % of the time. Mid career welders will have defects 2.5% of the time. New welders will have defects 6% of the time. The manufacturer employs 60% senior welders, 30% mid career welders and 10% new welders.
If an item is randomly chosen and found defective, what is the probability that it was produced by a new welder?