Some Definitions to Keep in
• OUTCOMES…are the possible results of
• an EVENT is any outcome OR group of
Ex: in rolling two dice, rolling a sum of
4 is an event corresponding two three
• If its random,
if you can’t predict what is going to
happen out of all of the possible
then any outcome is
EQUALLY LIKELY to occur.
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
Here is an Example:
• Find P(rolling an even number) with one
: how many favorable out comes are there?
: how many possible outcomes?
: make a ratio.
P(rolling an even number) = 3/6 or ½.
Try These: Using a Standard Dice
• P(odd number):
• P(5 or 6):
0 to 1 in any Probability
• All probabilities range from zero to one.
• Kinda like decimals and fractions and
0.5, ½, 1:2
Equally likely as
More likelyLess likely
Certain EventImpossible Event
• 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
• So, the probability of an event, plus the
probability of its complement, ALWAYS
• In the United States, the probability that a
child is a twin is 2 in 90, or 2/90. Find P(not
• 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.
• When you roll a dice, what is P(not 2)?
• What is the complement of an impossible
Finding the OddsFinding the Odds
• If PROBABILITY is a ratio of
• 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.
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?
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?