# How to find probability of some simple events?

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This pdf teaches how we can calculate the probability of some of the simple events and what vocabulary is used for calculating the probability of any random event.
1. of Simple
Events
2. Probability of Simple Events
 Life is full of random events!
 You need to get a "feel" for
them to be a smart and
successful person.
 The toss of a coin, throw of a
dice and lottery draws are all
examples of random events.
3. Probability of Simple Events
Students will be able to find the probability of a
simple event.
Students will be able to understand the
distinction between simple events and
compound events.
Essential Question:
(1) How do I find the probability of a simple
event?
(2) How can I distinguish between a simple and
compound event?
4. Probability of Simple Events
Vocabulary: Some words have special meaning in
Probability
Experiment or Trial: an action where the result is
uncertain.
Outcome: one possible result of an experiment.
Simple Event: a specific outcome, just one of the
possible outcomes.
Sample Space: the list of possible outcomes
Random: outcomes that occur at random if each
outcome is equally likely to occur.
Complementary Events: the events of one outcome
happening (E) and that outcomes not happening
( not E) are complimentary or opposite; the sum of
the probabilities of complementary events is 1.
5. Probability of Simple Events
Probability is the measure of the
likelihood that an event will occur
Probability does not tell us exactly what will
happen, it is just a guide
It is the ratio of
number of favorable outcomes
to the
total number of possible outcomes
6. CLASSICAL PROBABILITY
number of favorable outcomes
P(Event) = number of possible outcomes
Two Hypothesis :
Equally likely outcomes and Finished outcomes
Property
The probability is a number between 0 and 1
The probability of the certain event is 1
The probability of the impossible event is 0
in symbols:
7. Classical PROBABILITY
The probability of an Event can be
 as a FRACTION : 1/4
 as Unitary PERCENTAGE
between 0 and 1 : 0.25
 as a PERCENTAGE
between 0% to 100% : 25%
8. Probability of Simple Events
PROBABILITY LINE
0% 25% 50% 75% 100%
0 ¼ or .25 ½ 0r .5 ¾ or .75 1
Impossible Not Very Equally Likely Somewhat Certain
Likely Likely
9. Examples
that use Probability
1) Flip a Coin,
2) Roll a Dice,
3) Spinners
4) Pick a card from a deck of 52 Cards
5) Choose at ramdom a ball from a box
10. Probability of Simple Events
Example 1: Flip a coin - Tossing a Coin
What is the probability of flipping a tail?
When a coin is tossed, there are two possible outcomes:
P(event ) = # favorable outcomes
# possible outcomes
1 1
P(tail) = =
2 2
The probability is 1 out of 2 or .5 or 50%
Also… the probability of flipping a HEAD is ½.
11. TREE
Example 1
DIAGRAMM - FLIP A COIN
the sample space of events can be represented by
a tree diagram:
There are two
The probability of each branch
is written on the branch
The outcome is written at the
end of the branch
Notes: the SUM of the probabilities
of the individual events is ONE ( Total Probability )
12. Here is a tree diagram for the toss
of a coin:
13. Probability of Simple Events
Example 2: Roll a dice - Throwing Dice
a) What is the probability of rolling a 4 ?
# favorable outcomes
P(event) =
# possible outcomes
1
P(rolling a 4) =
6
The probability of rolling a 4 is 1 out of 6
When a single dice is thrown, there are six possible outcomes
The probability of any one of them is 1/6 !
14. Example 2: Roll a dice.
b) What is the probability of rolling an even
number? ( or an odd number)
P(event) = # favorable outcomes
# possible outcomes
3 1
P(even #) = =
6 2
The probability of rolling an even number ( or an odd
number ) is 3 out of 6 or .5 or 50%
15. TREE DIAGRAMM
ROLL A DICE
on the branches
you must write
the probability
Notes: the SUM of the probabilities
of the individual events is 1 ( Total Probability)
16. Spinners
Example 3:.
What is the probability of spinning green?
P(event) = # favorable outcomes
# possible outcomes
1 1
P(green) = =
4 4
The probability of spinning green is 1 out of 4
or .25 or 25%
17. Pick a card from a Deck of
Example 4: 52 Cards
A deck of 52 cards includes thirteen ranks of
each of the four suits :
hearts (♥) , diamonds (♦) spades (♠) and clubs (♣)
Each suit has 10 numbered cards
and 3 figures : jack, queen and king.
18. Pick a card from a Deck of
Example 4
52 Cards
What is the probability of picking a heart?
# favorable outcomes 13 1
P(heart) = = =
# possible outcomes 52 4
The probability of picking a heart is
1 out of 4 or .25 or 25%
What is the probability of picking a not heart?
# favorable outcomes 39 3
P(nonheart) = = =
# possible outcomes 52 4
3 out of 4 or .75 or 75%
“heart” and “Not heart” are complementary (opposite) events !
P(notE) = 1- P(E)
19. Choose at random a
ball from the box
Example 5:
A box contains 5 red balls, 3 green balls and 2
yellow balls. What is the probability of :
a) choose at random a green ball?
# favorable outcomes 3
P(green) = =
# possible outcomes = 10
3 out of 10 or .3 or 30%
b) choose at random a red ball?
# favorable outcomes 5
P(red) = =
# possible outcomes 10 or .5 or 50%
20. Example 5: TREE DIAGRAMM
Chose at random a ball from the bag
Red Green Yellow
notes: the SUM of the probabilities of the
individual events is ONE (Total Probability)