An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent 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%, 60%, and 40%, 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 ?

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