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: $P(\text{Face card or Club}) = \frac{11}{26}.$

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.