15.3 Exercise 22

The number N of customers in a shop in a given day is Poisson (120). Customers pay with cash or by MasterCard or Visa charge cards, with respective probabilties 0.25, 0.40, 0.35. Make the usual independence assumptions. Let N₁, N₂, N₃ be the numbers of cash sales, MasterCard charges, Visa card charges, respectively. Determine $P \left(N_{1} \geq 30\right)$, $P \left(N_{2} \geq 60\right)$, $P \left(N_{3} \geq 50\right)$, and $P \left(N_{2} > N_{3}\right)$.