Jun 14, 2024

**Topic**: Exploring probability and defining odds**Focus**: Calculating odds in favor and odds against using probability

**Event**: The occurrence we are interested in (e.g., winning the gray cup)**Probability of Event (A)**:- Given as 25% or 0.25 (can also be written as 1/4)

**Complement of Event (A')**:- The event not occurring
- Notated as A' or A-bar
- Probability of Complement (A'): 1 - P(A) = 3/4

**Odds in Favor**:- Calculated as: P(A) / P(A')
- Example: If P(A) = 1/4 and P(A') = 3/4
- Odds in favor = (1/4) / (3/4) = 1/3
- Simplified to: 1 to 3

**Odds Against**:- Calculated as: P(A') / P(A)
- Example: Using the same P(A) and P(A') as above
- Odds against = (3/4) / (1/4) = 3/1
- Simplified to: 3 to 1

**Scenario**: Mario chooses a single card from a standard deck where all hearts are in Janara's hand**Face Cards**: Jack, Queen, King of hearts**Total Hearts**: 13**Face Cards**: 3**Non-Face Cards**: 10**Odds in Favor**:- Probability of face card = 3/13
- Probability of non-face card = 10/13
- Odds in favor = 3 to 10

**Scenario**: What are the odds against a randomly chosen day being Sunday?**Probability of Sunday**: 1/7**Probability of Not Sunday**: 6/7**Odds Against**:- Odds against = 6/1
- Which is: 6 to 1

**Scenario**: Determining the probability from given odds**Odds Against**: 57 to 43 that a student is not in the first year**Calculating Probability**:- Adds up odds to get total outcomes: 57 + 43 = 100
- Probability of being in the first year = 43/100 = 43%

**Scenario**: Deciding who should take the shot based on past success rates**Ellen**: 8 goals out of 13 attempts (Probability: 0.615)**Brittany**: 10 goals out of 17 attempts (Probability: 0.588)**Josie**: 2 goals out of 3 attempts (Probability: 0.667)**Decision**: Based on highest probability or consistency (Ellen)

**Scenario**: Comparing odds against winning two games**Bim**: Odds against = 5 to 2 (converts to odds in favor = 2 to 5)**Zap**: Odds against = 7 to 3 (converts to odds in favor = 3 to 7)**Probabilities**:- Winning Bim: 2/7 = 0.286
- Winning Zap: 3/10 = 0.3

**Decision**: Higher probability of winning Zap

**Odds in Favor**: P(A) / P(A')**Odds Against**: P(A') / P(A)**Clarification**: Odds are not the same as probability ratios; total outcomes cancel out in odds

**Upcoming Topics**: Counting methods, set theory, and notation for solving more complicated probabilities

Thanks for watching!