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The sample space for different ratings of food is given in the table below:

Sample Space

For the rating by two person, what is the probability that one of the two will rate the meal as excellent and the other will rate it as good?

Any hint(s) for this question is appreciated.

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Assuming that each person's rating is independent of another person's rating, this can be solved using the notion of independence. Some hints:

if event A and event B are independent:

1) P(event A occurring AND event B occurring) = P(event A occurring) $\times$ P(event B occurring)

2) Be careful though, in this question, they don't specify who is person A and who is person B. That is, either person could be A or B. This adds a slight wrinkle that you need to be aware of. For example, imagine Joe is person A and Jane is person B. But Joe can also be person B and Jane could be person A.

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