Poisson process/probability

Question

Calls are distributed according to Poisson process at an average rate of 12 calls per hour. Calls are usually handled at the basic sales level, but if there is a more complicated case, the manager will need to be involved. The probability that an incoming call will require a manager is 0.5 and it is independent of the other calls. What is the probability to receive at least one call in 10 minutes time?

Answer 1

P(at least one call)= 1 - P(no calls for manager) = 1 - ((0.5 x 0.2)^0 x e^(0.5x0.2)/0!) = 1 - 0.367879441 = 0.632121