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A restaurant has four bottles of a certain wine in stock. The wine steward does not know that two of these bottles (Bottles 1 and 2) are bad. Suppose that two bottles are ordered, and the wine steward selects two of the four bottles at random. Consider the random variable x = the number of good bottles among these two.
a. One possible experimental outcome is (1, 2) (Bottles 1 and 2 are selected) and another is ( 2, 4). List all possible outcomes.
b. What is the probability of each outcome in Part (a)?
c. The value of x for the (1, 2) outcome is 0 (neither selected bottle is good), and x = 1 for the outcome (2, 4). Determine the x value for each possible outcome. Then use the probabilities in Part (b) to determine the probability distribution of x. |
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