Final answer:
The domain of x, which is the count of queens selected in a card-drawing experiment until the Queen of Hearts appears, is the set of all non-negative integers since there is no predetermined limit to the number of times the cards can be drawn with replacement.
Step-by-step explanation:
The student is asking about a geometric probability experiment involving the selection of playing cards from a standard 52-card deck. Specifically, they want to know the domain of the variable x, which represents the number of queens selected when drawing cards with replacement until the Queen of Hearts is drawn. A standard deck consists of four suits: clubs, diamonds, hearts, and spades, with 13 cards in each suit.
The domain of x in this experiment can be explained as follows. Since the experiment involves drawing cards with replacement, the Queen of Hearts could theoretically be drawn on any draw; therefore, there is theoretically no upper limit to how many times you could draw and not receive the Queen of Hearts. However, practically speaking, the domain is often considered as the set of non-negative integers. This is because one cannot draw a negative number of queens, and drawing continues until the Queen of Hearts is selected. Therefore, the domain of x is {0, 1, 2, 3, ...}, representing all possible non-negative integer counts of queens selected before drawing the Queen of Hearts.