Question 976927: 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:
= chocolate chosen
= strawberry chosen
= vanilla chosen
= ice cream on a cone
ice cream in a cup
Find the probability that the ice cream was strawberry flavor, given that it was sold on a cone
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Let's think of what happens for every  servings of ice cream sold.
For every servings of ice cream sold,
 , or  are chocolate,
 , or  are strawberry,
and the remaining  , or  are vanilla.
Of the  servings of chocolate ice cream sold,
 , or  were served in cones,
while the other  were served in cups.
Of the  servings of strawberry ice cream sold,
 , or  were served in cones,
while the other  were served in cups.
Of the  servings of vanilla ice cream sold,
 , or  were served in cones,
while the other  were served in cups.
We knew, without calculations that
the probability of a serving being chocolate is  ,
the probability of a serving being strawberry is  , and
the probability of a serving being vanilla is  .
Since out of servings, there were
 chocolate ice cream cones,
 strawberry ice cream cones, and
 vanilla ice cream cones,
the total number of cones served was  .
So, the probability of a serving being a cone is  .
Of course, that makes the probability of a serving being ice cream in a cup
 .
Since of the  cones served,
were strawberry ice cream cones,
the probability that the ice cream was strawberry flavor, given that it was sold on a cone is
 (rounded).
, , and 40%,
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