Problem 3 A manufacturing firm uses an automated system to produce bolts of the correct length. The firm executes three manufacturing runs in a day, each day's production requires skilled technicians to fine tune the system once in the morning. Every fine-tuning is independent of fine-tuning of the previous day. If the system is properly fine-tuned, the manufacturing run produces bolts with a 1% chance that they are not of the correct length. However, if not properly fine- tuned it produces bolts with a 3% chance that they are not of the correct length. Past experience suggests that there is 90% probability that the skilled technicians can properly fine-tune the system for each day. The firm recently hired some new skilled technicians in its workforce. On a particular manufacturing day, the firm produced bolts of incorrect length in one of the three manufacturing runs. Based on this information what is the revised probability that the firm's skilled technicians can properly fine-tune the system