# Two randomly selected grocery store patrons are each asked to take a blind taste test and to the state which of three diet colas he or she prefers.

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Two randomly selected grocery store patrons are each asked to take a blind taste test and to the state
which of three diet colas (marked as A, B, or C) he or she prefers.
a Draw a tree diagram depicting the sample space outcomes for the test results.
b List the sample space outcomes that correspond to
each of the following events:
(1) Both patrons prefer diet cola A.
(2) The two patrons prefer the same diet cola.
(3) The two patrons prefer different diet colas.
(4) Diet cola A is preferred by at least one of the
two patrons.
(5) Neither of the patrons prefers diet cola C.
c Assuming that all sample space outcomes are
equally likely, fnd the probability of each of the
events given in part b. Note that there are nine possible selections and so the sample space can be listed as

 Grocery 1 Grocery II A A A B A C B A B B B C C A C B C C

A tree diagram can be drawn for this space, representing all the possible selections as shown below. Both patrons prefer diet cola A = 1/3 * 1/3 = 1/9

That the two prefer the same diet of Cola, the probability space for this is represented by; AA or BB or CC

Hence the probability is 1/9 or 1/9 or 1/9 = 3/9 ~ 1/3

Prefer difference cola diets, this probability can be obtained by subtracting the probability of both persons prefering the same diet from one.

Probability that both groceries prefer different cola diets;-  1 - 1/3  = 2/3

Alternatively, this probability can be obtained by summing the above probabilities from the tree diagram, the probabilities represented by,-

AB, AC, BA, BA, CA,CB

Which means, 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 = 6/9 = 2/3

That diet A is prefered by at least one of the patrons, the probability space is composed by the events that either one or both patrons select cola A.

AA, or AB, or AC, or BA, or CA , probability = 1/9 or 1/9 or 1/9 or 1/9 or 1/9 = 5/9

That neither of the patrons select Cola C, should be AA, AB, BA, BB,