5. According to a pizza restaurant manager's experience, the number of toppings ordered for a large pizza, X, has the following probability distribution:

x 1 2 3

p(x) 0.5 0.3 0.2

(1) Suppose 2 large pizzas are ordered at random in this restaurant. What is the probability that the total number of toppings is smaller than 4?

(2) Suppose 5 large pizzas are ordered at random in this restaurant. What is the probability that at most 2 of them are ordered with exact 1 topping?

[Hint: the number of toppings could be classified as "1 topping" and "not 1 topping".]

(3) Suppose 100 large pizzas are ordered at random in this restaurant. What is the probability that the total number of toppings is greater than 177? [Hint: total number = n * average number]