Joe loves to eat out in area restaurants. His favorite foods are Mexican, Italian, Chinese, and Thai. On the average, Joe pays $10 for a Mexican meal, $15 for an Italian meal, $9 for a Chinese meal, and $11 for a Thai meal. Joe’s eating habits are predictable: There is a 70% chance that today’s meal is a repeat of yesterday’s, and equal probabilities of switching to one of the remaining three. 

(a) How much does Joe pay on the average for his daily dinner? 

(b) How often does Joe eat Mexican food?

(c) How many days later on average does Joe goes back to the Mexican restaurant for the first time after his last visit?