This document defines probability and odds ratios. It explains that odds are a ratio that compares favorable outcomes to non-favorable outcomes or vice versa. Several examples are provided to illustrate odds in favor of or against certain outcomes occurring, such as rolling a die, tossing a coin, or drawing a card from a deck. The document also provides an example of calculating the odds against picking a $20 bill from a wallet containing different bills.

1. PROBABILITY AND ODDS

2. RECALL:
A RATIO is a comparison of two numbers, similar to a fraction...
0.25
1:4 1/4
5:10 .... reduces to... 1:2

3. ODDS IN FAVOUR:
The RATIO of favorable outcomes to non­favorable outcomes.
FAVORABLE OUTCOMES : NON­FAVORABLE OUTCOMES
results you don't want
results you want
EX Roll a die. What are the odds in favour of rolling a 6?

4. ODDS AGAINTS:
The RATIO of non­favorable outcomes to favorable outcomes.
NON­FAVORABLE OUTCOMES : FAVORABLE OUTCOMES
results you want
results you don't want
EX Roll a die. What are the odds against rolling a 3?

5. EX Tossing a coin...
What are the odds against tossing heads?
What are the odds in favour of tossing tails?

6. From a deck of cards, what are the ....
odds in favour of drawing a club?
odds against drawing a King?
odds in favour of drawing a red card?
odds against drawing a black 7?

7. EX A wallet contains five $10 bills, two $5 bills and three $20 bills.
What are the odds against picking out $20 bill?
# of bills that are NOT $20 : # of bills that are $20
# of bills = 5 + 2 + 3 = 10 bills total
3 of them are $20 and 7 of them are NOT $20

8. HOMEWORK
p.337; #1­11