To find the probability that each card drawn is a three, we need to analyze the events in sequence. Since Mark draws a card, returns it to the deck, and then draws a second card, the events are independent, and the probability for each draw remains the same.

Step-by-Step Solution:

1. Determine the Total Number of Cards:
   There are 52 cards in a standard deck.

2. Determine the Number of Threes in the Deck:
   In a standard deck, there are 4 cards with the value of three (one for each suit: clubs, diamonds, hearts, and spades).

3. Calculate the Probability of Drawing a Three:
   For the first draw, the probability that Mark draws a three is: $\frac{\text{Number of Threes}}{\text{Total Number of Cards}} = \frac{4}{52} = \frac{1}{13}$

4. Repeat for the Second Draw:
   Since Mark returns the card to the deck, the probability remains the same for the second draw. The probability that he draws a three on the second draw is also $\frac{1}{13}$.

5. Calculate the Combined Probability:
   Since the events are independent, multiply the probabilities of each event: $P(\text{First card is a three and second card is a three}) = \frac{1}{13} \times \frac{1}{13} = \frac{1}{169}$

Answer:

The probability that each card drawn is a three is: $\frac{1}{169}$

Would you like more details, or do you have any questions?

Here are five related questions to explore:

1. What would the probability be if the deck were not reset between draws?
2. How would the probability change if Mark drew three cards in a row, each time replacing the card?
3. What is the probability of drawing two red cards in a row, with replacement?
4. If Mark draws two cards without replacement, what is the probability that they are both threes?
5. How would you calculate the probability of drawing two face cards in a row, with replacement?

Tip: For independent events, remember that you can multiply the probabilities to get the overall probability of both events occurring.