To find the probability of drawing a face card or a red card from a well-shuffled deck, we can use the principle of inclusion-exclusion.

Step 1: Calculate the total number of cards in a deck.

• A standard deck has 52 cards.

Step 2: Determine the number of face cards.

• There are 3 face cards (Jack, Queen, King) in each of the four suits: Hearts, Diamonds, Clubs, and Spades.
• Total number of face cards: $3 \times 4 = 12$.

Step 3: Determine the number of red cards.

• There are 26 red cards (13 Hearts + 13 Diamonds).

Step 4: Find the number of red face cards.

• There are 6 red face cards (3 Hearts + 3 Diamonds).

Step 5: Apply the inclusion-exclusion principle.

• The probability of drawing a face card or a red card is given by:

$P(\text{Face or Red}) = P(\text{Face}) + P(\text{Red}) - P(\text{Red Face})$

Where:

• $P(\text{Face}) = \frac{12}{52}$
• $P(\text{Red}) = \frac{26}{52}$
• $P(\text{Red Face}) = \frac{6}{52}$

Step 6: Substitute the values and calculate.

$P(\text{Face or Red}) = \frac{12}{52} + \frac{26}{52} - \frac{6}{52} = \frac{32}{52} = \frac{8}{13}$

Final Answer:

The probability of drawing a face card or a red card from a well-shuffled deck is $\frac{8}{13}$, or approximately 0.615.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. What is the probability of drawing a red face card?
2. What is the probability of drawing a black card?
3. What is the probability of drawing a non-face card?
4. If you draw two cards, what is the probability that both are face cards?
5. How does the probability change if a joker is added to the deck?

Tip: When calculating probabilities involving "or" conditions, remember to account for any overlap between the events to avoid double-counting.