Here is a table showing all 52 cards in a standard deck. Face cards Color Suit Ace Two Three Four Five Six Seven Eight Nine. Ten Jack Queen King Red Hearts A 10 Red Diamonds A 2♦ JQ K Black Spades Ac Q K Black Clubs A 10 Q K Suppose one card is drawn at random from a standard deck. (a) Find the odds in favor of drawing a red three. 0:0 ☐ to 0 (b) Find the odds against drawing a face card. 0 ?

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### Standard Deck of 52 Cards

Below is a table displaying all 52 cards in a standard deck, categorized by color, suit, and rank:

| Color | Suit      | Ace | Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Face Cards |
|-------|-----------|-----|-----|-------|------|------|-----|-------|-------|------|-----|------------|
| Red   | Hearts    | A♥  | 2♥  | 3♥    | 4♥   | 5♥   | 6♥  | 7♥    | 8♥    | 9♥   | 10♥ | J♥ Q♥ K♥   |
| Red   | Diamonds  | A♦  | 2♦  | 3♦    | 4♦   | 5♦   | 6♦  | 7♦    | 8♦    | 9♦   | 10♦ | J♦ Q♦ K♦   |
| Black | Spades    | A♠  | 2♠  | 3♠    | 4♠   | 5♠   | 6♠  | 7♠    | 8♠    | 9♠   | 10♠ | J♠ Q♠ K♠   |
| Black | Clubs     | A♣  | 2♣  | 3♣    | 4♣   | 5♣   | 6♣  | 7♣    | 8♣    | 9♣   | 10♣ | J♣ Q♣ K♣   |

### Probability Questions

**Suppose one card is drawn at random from a standard deck.**

(a) **Find the odds in favor of drawing a red three.**

(b) **Find the odds against drawing a face card.**

#### Instructions for Answering:
1. For part (a), count the number of red threes in the deck and compare it to the total number of cards.
2. For part (b), count the number of face cards in the deck and determine the odds against drawing one.

Use the following odds notation format: \( \text{a} : \text{b} \).

You may apply appropriate statistical and combinatorial techniques to solve
Transcribed Image Text:### Standard Deck of 52 Cards Below is a table displaying all 52 cards in a standard deck, categorized by color, suit, and rank: | Color | Suit | Ace | Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Face Cards | |-------|-----------|-----|-----|-------|------|------|-----|-------|-------|------|-----|------------| | Red | Hearts | A♥ | 2♥ | 3♥ | 4♥ | 5♥ | 6♥ | 7♥ | 8♥ | 9♥ | 10♥ | J♥ Q♥ K♥ | | Red | Diamonds | A♦ | 2♦ | 3♦ | 4♦ | 5♦ | 6♦ | 7♦ | 8♦ | 9♦ | 10♦ | J♦ Q♦ K♦ | | Black | Spades | A♠ | 2♠ | 3♠ | 4♠ | 5♠ | 6♠ | 7♠ | 8♠ | 9♠ | 10♠ | J♠ Q♠ K♠ | | Black | Clubs | A♣ | 2♣ | 3♣ | 4♣ | 5♣ | 6♣ | 7♣ | 8♣ | 9♣ | 10♣ | J♣ Q♣ K♣ | ### Probability Questions **Suppose one card is drawn at random from a standard deck.** (a) **Find the odds in favor of drawing a red three.** (b) **Find the odds against drawing a face card.** #### Instructions for Answering: 1. For part (a), count the number of red threes in the deck and compare it to the total number of cards. 2. For part (b), count the number of face cards in the deck and determine the odds against drawing one. Use the following odds notation format: \( \text{a} : \text{b} \). You may apply appropriate statistical and combinatorial techniques to solve
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