INTRO TO
PROBABILITY
PROBABILITY OF SIMPLE EVENTS
• The probability of an event is a measure of the likelihood
that the event will occur. Statisticians have agreed on
the following rules and conventions.
• The probability of any event can range from 0 to 1.
• The sum of probabilities of all sample points in a sample
space is equal to 1.
• The probability of event A is the sum of the probabilities
of all the sample points in event A.
• The probability of event A is denoted by P(A).
• Thus, if event A were very unlikely to occur, then P(A)
would be close to 0. And if event A were very likely to
occur, then P(A) would be close to 1.
PROBABILITY OF SIMPLE EVENTS
What is a PROBABILITY?
P(event) =
number of favorable outcomes
number of possible outcomes
Examples that use Probability:
(1) Dice, (2) Spinners, (3) Coins, (4) Deck of
Cards, (5) Evens/Odds, (6) Alphabet, etc.
• EVENT
A set of outcomes of an experiment (a subset of the sample
space) to which a probability is assigned.
• OUTCOME
• A possible result of an experiment.
PROBABILITY OF SIMPLE EVENTS
What is a PROBABILITY?
0%
25%
50%
75%
100%
0
¼ or .25
½ 0r .5
¾ or .75
1
Impossible
Not Very
Likely
Equally Likely
Somewhat
Likely
Certain
PROBABILITY OF SIMPLE EVENTS
Example 1: Roll a dice.
What is the probability of rolling a 4?
P(event)
# favorable outcomes
= # possible outcomes
P(rolling a 4) =
1
6
The probability of rolling a 4 is 1 out of 6
PROBABILITY OF SIMPLE EVENTS
Example 2: Roll a dice.
What is the probability of rolling an even
number?
P(event)
# favorable outcomes
= # possible outcomes
P(even #) =
3
6
=
1
2
The probability of rolling an even number is
3 out of 6 or .5 or 50%
PROBABILITY OF SIMPLE EVENTS
Example 3: Spinners.
What is the probability of spinning green?
P(green) =
Example 4: Flip a coin.
What is the probability of flipping a tail
on a fair coin?
P(tail) =
PROBABILITY OF SIMPLE EVENTS
Example 5: Deck of Cards.
What is the probability of picking a heart?
P(heart) =
# favorable outcomes
=
13
=
# possible outcomes
52
The probability of picking a heart is
1 out of 4 or .25 or 25%
1
4
What is the probability of picking a non heart?
P(nonheart) =
# favorable outcomes
=
39
# possible outcomes
52
The probability of picking a heart is
3 out of 4 or .75 or 75%
=
3
4
• ODDS
• The odds are defined as the probability that the
event will occur divided by the probability that the
event will not occur
• COMPLEMENT
• The complement of any event A is the event [not
A], the event that A does not occur. The event A
and its complement [not A] are mutually exclusive
and exhaustive.
PROBABILITY OF SIMPLE EVENTS
Example 5: Deck of Cards.
What is the probability of picking a heart?
P(heart) =
# favorable outcomes
=
13
=
# possible outcomes
52
The probability of picking a heart is
1 out of 4 or .25 or 25%
1
4
What is the probability of picking a non heart?
P(nonheart) =
# favorable outcomes
=
39
# possible outcomes
52
The probability of picking a heart is
3 out of 4 or .75 or 75%
=
3
4