One card is selected at random from a standard deck, then replaced, and a second card is drawn. Find the probability of selecting two face cards.

Sure, here is the step by step solution:

1. A standard deck of cards has 52 cards: 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace through 10, and the face cards Jack, Queen, King).

2. The face cards are the Jack, Queen, and King, which are 3 cards in each suit. So, there are 3 face cards/suit x 4 suits = 12 face cards in a deck.

3. The probability of drawing one face card from the deck is the number of face cards divided by the total number of cards, or 12/52 = 0.23076923076923078.

4. Because the card is replaced, the deck is back to 52 cards for the second draw, and the probability of drawing a face card remains the same, 12/52 = 0.23076923076923078.

5. The probability of both events happening (drawing a face card, replacing it, then drawing another face card) is the product of the probabilities of each event. So, the probability of drawing two face cards with replacement is 0.23076923076923078 x 0.23076923076923078 = 0.05325443786982249, or approximately 0.0533 or 5.33% when rounded to four decimal places or two decimal places respectively.