An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. 45% of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75 percent, 60 percent, and 40 percent, respectively. For a randomly selected sale, define the following events:

A1 = chocolate chosen
A2 = strawberry chosen
A3= vanilla chosen
B = ice cream on a cone
Bc = ice cream in a cup

a. Find the probability that the ice cream was sold on a cone and was vanilla flavor,

b. Find the probability that the ice cream was sold in a cup.

c. Find the probability that the ice cream was strawberry flavor, given that it was sold on a cone.

d. An ice cream sold happens to be sold in a cup, what's the probability that it was chocolate flavor ?