Question

Robot A, B and C make \(25\%\), \(35\%\) and \(40\%\) of circuit boards, with defect rates \(5\%\), \(4\%\) and \(2\%\) respectively. If one board is picked at random, what is the probability it is defective?

• A. 0.034
• B. 0.34
• C. 0.66
• D. 0.066

Hint:

When items come from multiple sources with different defect rates, weight each defect rate by the production share and add.

Answer 1

The Correct Option is A

By total probability: \[ P(\text{def}) = 0.25\cdot 0.05 + 0.35\cdot 0.04 + 0.40\cdot 0.02 = 0.0125 + 0.014 + 0.008 = 0.0345 \approx 0.034. \] \[ \boxed{0.034} \]