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Let's break down and solve the problem based on the image you've provided:

We are asked to find:

### (a) The probability that the card drawn is either a diamond or a face card.

- A standard 52-card deck has 4 suits (diamonds, hearts, spades, and clubs), with 13 cards in each suit.
- **Diamonds**: There are 13 diamond cards in the deck.
- **Face cards**: Each suit has 3 face cards (Jack, Queen, and King), so there are a total of \( 3 \times 4 = 12 \) face cards.

However, 3 of the face cards (Jack, Queen, and King of diamonds) are already counted in the diamond suit, so we should not double-count them.

Thus, the total number of cards that are either a diamond or a face card is:
\[
13 \ (\text{diamonds}) + 9 \ (\text{face cards that are not diamonds}) = 22
\]
So, the probability of drawing a diamond or a face card is:
\[
P = \frac{22}{52} = \frac{11}{26}
\]

### (b) The odds in favor of the event (drawing a diamond or a face card)

The odds in favor are calculated as the ratio of favorable outcomes to unfavorable outcomes:
- **Favorable outcomes**: 22 (from part a)
- **Unfavorable outcomes**: \( 52 - 22 = 30 \)

Thus, the odds in favor are:
\[
\text{Odds} = \frac{22}{30} = \frac{11}{15}
\]
So, the odds in favor of drawing a diamond or a face card are **11 to 15**.

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Would you like further details on any part of the solution or clarification on a particular concept?

Here are 5 related questions to deepen your understanding:

1. How would the probability change if you were asked to find the probability of drawing a red card or a face card?
2. What are the odds against drawing a diamond or a face card in the same scenario?
3. If you were drawing two cards without replacement, what would be the probability that both cards are diamonds or face cards?
4. How would the odds be affected if jokers were included in the deck?
5. What is the probability of drawing a heart or a numbered card (non-face card)?

**Tip:** When calculating probabilities involving overlapping events (like face cards in a suit), always subtract the overlap to avoid double-counting.

For the experiment of drawing a single card from a standard 52-card deck, find (a) the probability of the following event, and (b) the odds in favor of the following event: diamond or face card.

Calculate the probability and odds of drawing a diamond or a face card from a standard 52-card deck. This problem covers key probability concepts and formulas, including combinatorics, suitable for students in Grades 9-12.

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