A company has 3 employees. Each of them has an independent project and must work in city A for 7 days continuously every month. For the rest of month they work in City B. What is the probability that the three of them will be in city A at same time?
They start at random dates. Also, you can assume that there are always 30 days in a month.
I first treat the three as independent events. The probability of being in city A for each employee is $7/30$. Then I calculate at a day the probability of three people be in City A, which is $(7/30)^3$. But something is wrong, I think the probability should be greater than that.