Five people (Alex, Bill, Cathy, David, and Erica) form a club, N= {A, B, C, D, E}. Cathy and Erica are women, and the others are men. If they choose a secretar randomly, find the odds in favor of a person whose name begins with a vowel becoming secretary. The odds in favor of a person whose name begins with a vowel becoming secretary are to (Type whole numbers.)

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Five people (Alex, Bill, Cathy, David, and Erica) form a club, \(N = \{A, B, C, D, E\}\). Cathy and Erica are women, and the others are men. If they choose a secretary randomly, find the odds in favor of a person whose name begins with a vowel becoming secretary.

The odds in favor of a person whose name begins with a vowel becoming secretary are [   ] to [   ].

(Type whole numbers.)
Transcribed Image Text:Five people (Alex, Bill, Cathy, David, and Erica) form a club, \(N = \{A, B, C, D, E\}\). Cathy and Erica are women, and the others are men. If they choose a secretary randomly, find the odds in favor of a person whose name begins with a vowel becoming secretary. The odds in favor of a person whose name begins with a vowel becoming secretary are [   ] to [   ]. (Type whole numbers.)
### Probability and Odds

**Scenario:**
Annie randomly chooses a single ball from the can shown here. Find the odds against the event.

**Event:**
Drawing a yellow (Y) ball.

**Diagram Description:**
The can contains a total of 12 colored balls arranged in a 3x4 grid pattern. The distribution of colors is as follows:
- Red (R) balls: 4 
- Yellow (Y) balls: 3 
- Blue (B) balls: 5 

**Task:**
State the odds against picking a yellow ball in lowest terms.

**Solution:**
1. **Count the Yellow Balls:**  
   Number of yellow balls (Y) = 3

2. **Count the Non-Yellow Balls:**  
   Non-yellow balls (Red + Blue) = 4 (Red) + 5 (Blue) = 9

3. **Calculate the Odds Against Yellow:**  
   Odds against yellow = Non-yellow balls : Yellow balls  
   = 9 : 3

4. **Simplify the Odds:**  
   Simplify the ratio 9:3 to its lowest terms, which is 3:1.

**Result:**  
The odds against yellow are 3 to 1.

**Instruction:**  
Type whole numbers only in the answer boxes provided for odds.
Transcribed Image Text:### Probability and Odds **Scenario:** Annie randomly chooses a single ball from the can shown here. Find the odds against the event. **Event:** Drawing a yellow (Y) ball. **Diagram Description:** The can contains a total of 12 colored balls arranged in a 3x4 grid pattern. The distribution of colors is as follows: - Red (R) balls: 4 - Yellow (Y) balls: 3 - Blue (B) balls: 5 **Task:** State the odds against picking a yellow ball in lowest terms. **Solution:** 1. **Count the Yellow Balls:** Number of yellow balls (Y) = 3 2. **Count the Non-Yellow Balls:** Non-yellow balls (Red + Blue) = 4 (Red) + 5 (Blue) = 9 3. **Calculate the Odds Against Yellow:** Odds against yellow = Non-yellow balls : Yellow balls = 9 : 3 4. **Simplify the Odds:** Simplify the ratio 9:3 to its lowest terms, which is 3:1. **Result:** The odds against yellow are 3 to 1. **Instruction:** Type whole numbers only in the answer boxes provided for odds.
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