In a typical month, the demand for cement material in a city may be low (L), average (A), or high (H) with respective probabilities of 0.60, 0.30, and 0.10. The various suppliers of cement material in the city can definitely handle a low demand (L), but if the demand is average (A) or high (H), the supply may be inadequate with probabilities of 0.10 and 0.50, respectively.

a) What is the probability of shortage of cement material in a given month?

b) If a shortage occurred in a month, what is the probability that the demand had been average?

c) What is the probability of shortage of cement in at least 1 month over a two-month period? Assume that the demand in supply of cement material are statistically independent between consecutive months.