 Ifyou pick a card at random from a well shuffled deck what is the probabiliy that you get a face card or red card 

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.

If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or red card?

Learn how to calculate the probability of drawing a face card or a red card from a well-shuffled deck using the inclusion-exclusion principle. This detailed solution involves calculating the probabilities of face cards and red cards, accounting for overlap. Suitable for students in Grades 9-12.

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