This document defines key probability terms like outcomes, events, randomness, and equally likely outcomes. It explains how to calculate probability as a ratio of favorable outcomes to total possible outcomes. Examples are provided like finding the probability of rolling an even number on a standard six-sided die. The complement of an event is also defined as the opposite outcome. Finally, odds are defined as the ratio of favorable outcomes to unfavorable outcomes or vice versa.

1. Chapter 5, Section 6:
Probability & Odds

2. Some Definitions to Keep in
Mind
• OUTCOMES…are the possible results of
an action.
• an EVENT is any outcome OR group of
outcomes.
Ex: in rolling two dice, rolling a sum of
4 is an event corresponding two three
different outcomes.

3. Randomness
• If its random,
if you can’t predict what is going to
happen out of all of the possible
outcomes,
then any outcome is
EQUALLY LIKELY to occur.

4. Probability of an Event
• When outcomes are equally likely, you can
use a RATIO to find the PROBABILITY
OF AN EVENT.
• Probability of an Event = P(event) =
Number of favorable outcomes/number of
possible outcomes

5. Here is an Example:
• Find P(rolling an even number) with one
dice.
1st
: how many favorable out comes are there?
2nd
: how many possible outcomes?
3rd
: make a ratio.
P(rolling an even number) = 3/6 or ½.

6. Try These: Using a Standard Dice
• P(odd number):
• P(2):
• P(5 or 6):
1/2
1/6
1/3

7. 0 to 1 in any Probability
• All probabilities range from zero to one.
• Kinda like decimals and fractions and
ratios.
PROBABILITY
0.5, ½, 1:2
Equally likely as
unlikely
More likelyLess likely
Certain EventImpossible Event

8. Complement
• The COMPLEMENT of an event is the
OPPOSITE of that event.
• Example: P(rolling an even number), the
complement would be P(rolling an odd
number).
• So, the probability of an event, plus the
probability of its complement, ALWAYS
EQUALS 1.

9. Double Trouble
• In the United States, the probability that a
child is a twin is 2 in 90, or 2/90. Find P(not
a twin).
• P(twin) + P(not a twin) = 1 (Equation)
• 2/90 + P(not a twin) = 1 (Substitute)
• 2/90 – 2/90 + P(not a twin) = 1 – 2/90
– (Subtract from both sides)
• P(not a twin) = 88/90 = 44/45
• Every 44 out of 45 people are not a twin.

10. Try These
• When you roll a dice, what is P(not 2)?
• 5/6
• What is the complement of an impossible
event?

11. Finding the OddsFinding the Odds
• If PROBABILITY is a ratio of
PART:WHOLE,
• Then an ODD is the ratio of PART: PART.
Odds in Favor of an Event:
– # of FAVORABLE outcomes
– # of UNFAVORABLE outcomes.
Odds against an Event:
– # of UNFAVORABLE outcomes
– # of FAVORABLE outcomes.

12. Lets Try These
• What are the ODDS that a quarter shown at
random from these has a least one human
figure on it?
• What are the odds that a quarter chosen at
random from the five shows a horse?
• What are the odds that it shows no horse?

13. And This One
• Consider the event of randomly choosing a
quarter that shows the outline of a state.
• A) What are the odds in favor of the event?
• B) What are the odds against the event?