Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let Y1 denote the proportion of the capacity of the bulk tank that is available after the tank is stocked at the beginning of the week. Because of the limited supplies, Y1 varies from week to week. Let Y2 denote the proportion of the capacity of the bulk tank that is sold during the week. Because Y1 and Y2 are both proportions, both variables take on values between 0 and 1. Further, the amount sold, y2, cannot exceed the amount available, y1. Suppose that the joint density function for Y1 and Y2 is given by fy1y2(y,1y2) = { 3y1 0<= y2 <= y1 <= 1 and 0 otherwise
what is the probability that more than half a tank is sold given that three-fourths of a tank is stocked?
(show work please)