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Answer :
Final answer:
The sample space for selecting two cards at random with replacement from three unique cards, QQ, QR, QP, RQ, RR, RP, PQ, PR, PP, is represented by Option A. Each pair of letters reflects the possible two card selections, including scenarios with repeated selections.
Explanation:
The question asks us to identify the sample space for selecting two cards at random from a box containing three unique cards, which are a card with a question mark (Q), a rectangle (R), and a pear (P), with replacement.
This means that after selecting a card, it is replaced back into the box before selecting the second card.
Sample space is the set of all possible outcomes of an experiment. In this case, because the cards are returned to the box after each pick, every card is available for selection both times.
This leads to the following combinations when two cards are picked with replacement: QQ, QR, QP, RQ, RR, RP, PQ, PR, PP.
This includes scenarios where the same card can be picked twice, such as QQ or PP.
Based on the options provided, the correct option for the sample space is Option A: QQ, QR, QP, RQ, RR, RP, PQ, PR, PP.
Each possible outcome represents a pair of selections where the first letter corresponds to the first pick and the second letter corresponds to the second pick, considering that the same card can be picked again due to the replacement.
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