To calculate the odds of an event, you need to determine the ratio of favorable outcomes to unfavorable outcomes. In this case, the favorable outcomes refer to the event occurring, while the unfavorable outcomes refer to the event not occurring.
Let's calculate the odds for each event:
1. Choosing a girl:
- Favorable outcomes: There are 15 girls in the class.
- Unfavorable outcomes: There are 10 boys in the class.
- Odds in favor: The ratio of favorable to unfavorable outcomes is 15:10, which simplifies to 3:2 odds in favor of choosing a girl.
- Odds against: The ratio of unfavorable to favorable outcomes is 10:15, which simplifies to 2:3 odds against choosing a girl.
2. Choosing a boy:
- Favorable outcomes: There are 10 boys in the class.
- Unfavorable outcomes: There are 15 girls in the class.
- Odds in favor: The ratio of favorable to unfavorable outcomes is 10:15, which simplifies to 2:3 odds in favor of choosing a boy.
- Odds against: The ratio of unfavorable to favorable outcomes is 15:10, which simplifies to 3:2 odds against choosing a boy.
In summary, the odds in favor of choosing a girl are 3:2, while the odds against are 2:3. Conversely, the odds in favor of choosing a boy are 2:3, and the odds against are 3:2.