Of the 47 plays attributed to a playwright, 12 are comedies, 15 are tragedies, and 20 are histories. If one play is selected at random, find the odds in favor of selecting a comedy or history. The odds in favor are (Simplify your answer.) C
Of the 47 plays attributed to a playwright, 12 are comedies, 15 are tragedies, and 20 are histories. If one play is selected at random, find the odds in favor of selecting a comedy or history. The odds in favor are (Simplify your answer.) C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Of the 47 plays attributed to a playwright, 12 are comedies, 15 are tragedies, and 20 are histories. If one play is selected at random, find the odds in favor of selecting a comedy or a history.
---
**Solution:**
To find the odds in favor of selecting a comedy or a history, we need to calculate the total number of comedies and histories, and then compare it to the number of outcomes that are not comedies or histories (which are the tragedies).
1. **Number of Comedies:** 12
2. **Number of Histories:** 20
- **Total Comedies and Histories:**
\[
12 + 20 = 32
\]
3. **Number of Tragedies (not comedy or history):** 15
**Odds in favor** are calculated as the ratio of favorable outcomes to unfavorable outcomes.
\[
\text{Odds in Favor} = \frac{\text{Number of Comedies and Histories}}{\text{Number of Tragedies}} = \frac{32}{15}
\]
- **Simplified Odds:** The odds in favor are \(32:15\).
*Ensure to simplify further if possible, in this case, it’s already simplified.*
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a4d4bf4-ffa5-40bf-a4b6-a19d4afcfff5%2F7ddfcc7d-bc8b-49dc-844c-c27859c61684%2Fuddkemj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Of the 47 plays attributed to a playwright, 12 are comedies, 15 are tragedies, and 20 are histories. If one play is selected at random, find the odds in favor of selecting a comedy or a history.
---
**Solution:**
To find the odds in favor of selecting a comedy or a history, we need to calculate the total number of comedies and histories, and then compare it to the number of outcomes that are not comedies or histories (which are the tragedies).
1. **Number of Comedies:** 12
2. **Number of Histories:** 20
- **Total Comedies and Histories:**
\[
12 + 20 = 32
\]
3. **Number of Tragedies (not comedy or history):** 15
**Odds in favor** are calculated as the ratio of favorable outcomes to unfavorable outcomes.
\[
\text{Odds in Favor} = \frac{\text{Number of Comedies and Histories}}{\text{Number of Tragedies}} = \frac{32}{15}
\]
- **Simplified Odds:** The odds in favor are \(32:15\).
*Ensure to simplify further if possible, in this case, it’s already simplified.*
(Simplify your answer.)
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