Regis uses a fair deck of 52 different cards to determine the probability of drawing the same card twice in a row. He draws one card, replaces it, shuffles the deck, and draws another card. He records the results of the two draws.

Question

How many outcomes are in the sample space?

Answer 1

To determine the number of outcomes in the sample space when Regis draws a card twice from a full deck of 52 cards, we can break down the process as follows:

1. First Draw: When Regis draws the first card from the deck, he has 52 possible outcomes (one for each card).
2. Replacement: After the first draw, the card is replaced, and the deck is shuffled. This means that for the second draw, there are again 52 possible outcomes since the deck is back to its full complement of cards.

Since the two draws are independent (because the first card is replaced), we can find the total number of outcomes in the sample space by multiplying the number of outcomes for each draw:

\[ \text{Total outcomes} = (\text{Number of outcomes for the first draw}) \times (\text{Number of outcomes for the second draw}) = 52 \times 52 = 2704. \]

Thus, the total number of outcomes in the sample space is \( \boxed{2704} \).