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The image shows a probability problem related to a deck of 52 playing cards. Let’s solve the three parts step-by-step:

### (a) What is the probability that the card drawn is a face card?

Face cards are the Jack, Queen, and King in each suit. Each suit (Hearts, Diamonds, Spades, Clubs) has 3 face cards, so there are:
\[
3 \text{ face cards} \times 4 \text{ suits} = 12 \text{ face cards in total}.
\]
The total number of cards is 52, so the probability of drawing a face card is:
\[
P(\text{Face card}) = \frac{12}{52} = \frac{3}{13}.
\]

### (b) What is the probability that the card drawn is a club?

Each suit (Hearts, Diamonds, Spades, Clubs) has 13 cards. Therefore, the number of club cards is 13. The probability of drawing a club is:
\[
P(\text{Club}) = \frac{13}{52} = \frac{1}{4}.
\]

### (c) What is the probability that the card drawn is a face card or a club?

To find this probability, we need to use the principle of inclusion and exclusion:
\[
P(\text{Face card or Club}) = P(\text{Face card}) + P(\text{Club}) - P(\text{Face card and Club}).
\]

- \(P(\text{Face card}) = \frac{3}{13}\),
- \(P(\text{Club}) = \frac{1}{4} = \frac{13}{52}\),
- \(P(\text{Face card and Club})\): There are 3 face cards in the club suit (Jack, Queen, King of Clubs), so \(P(\text{Face card and Club}) = \frac{3}{52}\).

Now, calculating the combined probability:
\[
P(\text{Face card or Club}) = \frac{3}{13} + \frac{13}{52} - \frac{3}{52}.
\]

First, express \(\frac{3}{13}\) with denominator 52:
\[
\frac{3}{13} = \frac{12}{52}.
\]
Now, substitute:
\[
P(\text{Face card or Club}) = \frac{12}{52} + \frac{13}{52} - \frac{3}{52} = \frac{22}{52} = \frac{11}{26}.
\]

So, the probability of drawing a face card or a club is:
\[
P(\text{Face card or Club}) = \frac{11}{26}.
\]

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Would you like more details or have any questions about these solutions?

Here are 5 related questions:
1. What is the probability of drawing a red card from a standard deck?
2. How many face cards are in a red suit?
3. What is the probability of drawing a numbered card (2 through 10)?
4. What is the probability of drawing a non-face card that is a spade?
5. How would the probabilities change if jokers were included in the deck?

**Tip**: The principle of inclusion and exclusion helps to avoid double-counting in probability when events overlap.

Suppose one card is drawn at random from a standard deck. What is the probability that the card drawn is (a) a face card, (b) a club, (c) a face card or a club?

Learn how to calculate the probability of drawing a face card, a club, or either from a standard deck of 52 cards. This problem covers the basic concepts of probability and the inclusion-exclusion principle, suitable for Grades 6-8.

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