SOLUTION: please help me, i have submitted this question several times. susan forman has to purchase a box of cereal, a bottle dof soda, and a can of vegetables. the types of cereal, soda,

Question 489142: please help me, i have submitted this question several times.
susan forman has to purchase a box of cereal, a bottle dof soda, and a can of vegetables. the types of cereal, soda, and vegetable she is considering are below.
cereal: rice krispies, frosted flakes, honeycomb
soda:orange,black cherry, ginger ale.
vegetables: peas, carrots.
a)determine the number of points in the sample space.
b)construct a tree diagram and determine the sample space. determine the probability that she selects:
c) honeycomb for the cerel.
d)rice krispies and ginger ale.
e)a soda other than black cherry.
Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
The first step is to count the options in each category:
C: 3
S: 3
V: 2
a) Points in sample space = product of these 3 independent choice counts: 3*3*2 = 18.
b) From root of tree, 3 branches based on and labeled with a choice C.
Each of those 3 branches have 3 more, labeled with choice of S.
Each of those 9 branches have 2 more, labeled with choice of V.
Each of these 18 (see "a") terminal nodes are labeled with the 3 selections that were made along the path from root.
The total tree has 3 + 3*3 + 18 = 30 branches.
[that's what I would do, maybe you are supposed to do it differently].
Now the probabilies aren't known, so assume they are equal within categories.
c) 1/3
d) (1/3)*(1/3) = 1/9
e) ((3-1)/3) = 2/3

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