Liquefaction of sand could occur because of earthquakes. For simplicity, rate earthquake intensities into low ( L ) , medium ( M ) , and high ( H ) , and their probabilities are 0.9 , 0.09 , and 0.01 , respectively, once an earthquake occurs. The probability of liquefaction associated with these three intensities are 0.01 , 0.1 , and 0.9 , respectively. (1) What is the probability of liquefaction of sand during the next earthquake? (4/10) (2) If the liquefaction of sand occurs during an earthquake, what is the probability that the earthquake is medium? ( 4/10 ) (3) What is the probability that the sand will survive the next three earthquakes? (2/10).