CHAPTER 6 – Notes 6-3
- COMPARING PROBABILITY AND ODDS-
GOALS
· To calculate the odds in favour and odds against events occurring.
COMPARING PROBABILITY AND ODDS
· People make decisions based on odds every day: If you don’t study for a test the chances in favour of passing, compared to the chance of my not passing are 5:7.
· We want to make educated decisions in life, and so we need to know how to calculate the odds for and against events happening
TERMS:
P = # of desired outcomes
Total # of outcomes
ODDS IN FAVOUR = favourable outcomes:unfavourable outcomes
ODDS AGAINST = unfavourable outcomes : favourable outcomes
Total Outomes = favourable outcomes + unfavourable outcomes
Hints:
1. calculate probability first
2. try to have probability as a fraction
Example 1: When rolling a 6 sided die, determine the odds in favour of rolling a 4.
Solution:
Do Probability 1st.
P = # of desired outcomes
Total # of outcomes
P = 1
6
ODDS IN FAVOUR = favourable outcomes:unfavourable outcomes
Odds in Favour: 1 : ?
Odds in Favour: 1 : 5EXAMPLE 2
When drawing a card from a well-shuffled deck of playing cards, determine the odds in favour of drawing a diamond
Solution:
Do Probability 1st.
P = # of desired outcomes
Total # of outcomes
P = 1
4
ODDS IN FAVOUR = favourable outcomes:unfavourable outcomes
Odds in Favour: 1 : ?
Odds in Favour: 1 : 3
EXAMPLE 3
A wallet contains three $5 bills, two $10 bills, and one $20 bill. What are the odds against drawing out a $10 bill?
Solution:
Do Probability 1st.
P = # of desired outcomes
Total # of outcomes
P = 2 = 1
6 3
ODDS IN FAVOUR = favourable outcomes:unfavourable outcomes
Odds in Favour: 1 : ?
Odds in Favour: 1 : 2
Odds Against: 2 : 1
EXAMPLE 4
A survey of 320 students in your school reveals that 240 of them listen to radio station Star FM 98.3 Find the odds against randomly selecting a student who listens to this station:
Solution:
Do Probability 1st.
P = 240 = 24 = 12 = 6 = 3
320 32 16 8 4
Odds in Favour: 3 : ?
Odds in Favour: 3 : 1
Odds Against: 1 : 3
EXAMPLE 5
What is the probability, odds for and odds against of rolling two dies (dice) and getting an eleven or twelve?
Solution:
1st Write out all the combinations of dice
1-1 2-1 3-1 4-1 5-1 6-1
1-2 2-2 3-2 4-2 5-2 6-2
1-3 2-3 3-3 4-3 5-3 6-3
1-4 2-4 3-4 4-4 5-4 6-4
1-5 2-5 3-5 4-5 5-5 6-5
1-6 2-6 3-6 4-6 5-6 6-6
and figure out which combinations add up to 11 and 12
Do Probability next.
P = 3 = 1
36 12
Odds in Favour: 1 : ?
Odds in Favour: 1 : 11
Odds Against: 11 : 1
EXAMPLE
What is the probability, odds for and odds against of drawing a vowel in the word “smiling” if each letter was written on separate cards?
Smiling
Solution: Do Probability next.
P = 2
7
Odds in Favour: 2 : ?
Odds in Favour: 2 : 5
Odds Against: 5 : 2
Complete the text book assignment on pages 337- 339
Questions 1-10
Complete questions 1 and 7 to 10 in Note Helper 6-3. Complete questions 2 to 6 in your notebook.
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