A nail salon is deciding if appointing an additional manicurist will be financially feasible. Today, the nail salon has three manicurists, only one of whom is by appointment and the other two for drop-in sessions. The following tables summarize the various durations of time in a session and the time intervals between arrivals of customers, respectively:

The salon manager notices that if there is one customer waiting, the arriving customer has a probability of 0.6 of leaving, and if there are two customers waiting, the arriving customer has a probability of 0.9 of leaving. The manager also calculates the profit if she hires a new manicurist and if the new manicurist is busy for more than half of the time. Calculate the probability that appointing a new manicurist will generate a profit. The salon is open for 10–18 hours for 5 days a week.

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TIME PROBABILITY TIME PROBABILITY 30 0.1 10 0.1 45 0.2 20 0.2 60 0.4 30 0.4 75 0.2 45 0.2 90 0.1 50 0.1