Two methods A and B are available for teaching a certain industrial skill. The f

Question

Two methods A and B are available for teaching a certain industrial skill. The failure rate is 20% for A and 10% for B. However, B is more expensive and hence is used only 30% of the time (A is used the other 70 %). A worker was taught the skill by one of the methods but failed to learn it correctly. What is the probability that this worker was taught by method B? A worker was taught the skill by one of the methods but failed to learn it correctly. What is the probability that this worker was taught by method A? What is the probability that the worker succeeded to learn it correctly?

Explanation / Answer

a) we need to find that the probability the worker was taught by b

total failure probability = 0.7*0.2+0.3*0.1 = 0.17

the probability that failed by b = 0.3*0.1 = 0.03

hence the probability = 0.03/0.17 = 0.176

b) similarly as above

the total failure probability = 0.17

probability of fail by a = 0.7*0.2 = 0.14

hence probability = 0.14/0.17 = 0.823

c) the probability that the person learned it correctly = 0.7*0.8 + 0.3*0.9 = 0.83

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