Question

After production, an electrical circuit is given a quality score of A, B. C, or D. Over a certain period of time, 77% of the circuits were given a quality score A. 11% were given a quality score B, 7% were given a quality score C, and 5% were given a quality score D. Furthermore, it was found that 2% of the circuits given a quality score A eventually failed, and the failure rate was 10% for circuits given a quality score B. 14% for circuits given a quality given a quality score C, and 25% for circuits given a quality score D. Show all your work and circle your final answers. Use four decimal places for your calculations. a) Find the probability of a circuit failing. b) If a circuit failed, what is the probability that it had received a quality score either C or D?

Answer 1

a) 0.0125

b) 0.4579

Explanation:

For this question use tree diagram method to solve the question or by simply listing down the probabilities as I have done in the attached picture. Firstly, we need to convert all percentages in to decimal and those decimals will represent probability of each event. For example if we consider probability of quality score A it can be found by diving 77 with 100:

77/100 = 0.77

Similarly all probabilities can be found by simply dividing percentages with 100.

Part (b) is a conditional probability question. Given that a circuit failed is the condition. So we need to use conditional probability method to solve it.