A surprising invention

An inventor has made a fantastic new machine that can do many household chores. But what the inventor doesn't know is that he accidentally coded the machine to have a \(\frac{1}{6}\) chance of dusting the house, \(\frac{1}{3}\) chance of watering the garden and a \(\frac{1}{4}\) chance of cleaning the dishes. Every five minutes, the robot switches to do something new. So, by the end of one hour, how many times can we expect that the invention is going to clean the dishes?

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