Joe loves to eat out in area restaurants His favorite foods

Joe loves to eat out in area restaurants. His favorite foods are Mexican, Italian, Chinese, and Thai. On the average Joe pays $10.00 for a Mexican meal, $15.00 for an Italian meal, $9.00 for a Chinese meal, and $11.00 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?

Solution

His daily dinner payments would be

average of all 4 costs = 55/4 = 13.75

Selecting Mexian food out of 4 has prob =0.25

If yesterday Mexian food eaten today prob for eating = 0.25(0.70) = 0.175

If yesterday Medican not eaten today prob for eating = 0.75(0.30)(1/3) = 0.075

Hence prob for eating Mexian good = 0.250

Joe eats 1/4 times Mexian food as others.