2 cards were drawn. what is the probability of it being red or face card? TAKE NOTE: w repetition
a. 0.857
b. 0.758
c. 0.875
d. 0.578

Let's calculate the probability of drawing two cards, where each card is either a red card (hearts or diamonds) or a face card (jack, queen, or king) **with replacement**.

### Total Cards:
- A deck has 52 cards.

### Red Cards:
- There are 26 red cards (13 hearts and 13 diamonds).

### Face Cards:
- There are 12 face cards in total (3 face cards each for hearts, diamonds, clubs, and spades).

### Overlap (Red Face Cards):
- There are 6 face cards that are also red (3 in hearts and 3 in diamonds).

### Step 1: Probability of Drawing a Red or Face Card
We need to avoid double-counting the red face cards:
- The number of red or face cards is the sum of the red cards and face cards, minus the overlap (since red face cards are counted twice).

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

### Step 2: Probability for Two Draws (With Replacement)
Since the cards are drawn with replacement, the probability for both cards being red or face cards is simply:

\[
P(\text{Both Cards Red or Face}) = \left( \frac{8}{13} \right) \times \left( \frac{8}{13} \right) = \left( \frac{8}{13} \right)^2 = \frac{64}{169} \approx 0.758
\]

### Final Answer:
The probability is approximately **0.758**, which corresponds to **option b**.

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Do you want further details or have any questions?  
Here are 5 related questions to consider:

1. What is the probability of drawing two black face cards with replacement?
2. How would the probability change if there were no replacement of cards?
3. What is the probability of drawing two face cards consecutively?
4. What is the probability of drawing at least one red card in two draws?
5. How would the calculation change if the deck had jokers included?

**Tip:** Always watch for overlap (like red face cards) when counting probabilities of "either/or" events!

2 cards were drawn. What is the probability of it being red or a face card? Take note: with replacement. a. 0.857 b. 0.758 c. 0.875 d. 0.578

Calculate the probability of drawing two cards, where each is either red or a face card, with replacement. This problem covers key probability concepts and includes step-by-step solutions with detailed calculations. Ideal for high school students studying probability theory.

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