Here are the probabilities for the different scenarios: Odd: P(odd) = 7/15 Greater than 5: P(greater than 5) = 10/15 Even and less than 7: P(even and less than 7) = 2/15 Even or less than 7: P(even or less than 7) = 11/15

1. Give the Sample Space of the following events:
1. Throwing a fair coin. S = {H, T}
2. Throwing of two fair coins. S = {HH, TT, HT, TH}
3. Getting a ball from a pail containing 1 blue,1 green, 1
red and 1 orange balls. S = {red, orange, blue, green}
4. Forming a three – letter code from the letters B, V and
X. S = {BVX, BXV, VBX, VXB, XBV, XVB}
5. Choosing 1 letter at random from 5 vowels. S = {a, e, i,
o, u}
6. Choosing a prime number less than 15 at random. S =
{2, 3, 5, 7, 11, 13}

2. Give the possible outcomes for each event.
Given: S = {2, 4, 6, 8, 10, 12, 14, 16}
1. Getting a number divisible
by 3.
2. Getting a number less than
12.
3. Getting a number divisible
by 4.
4. Getting a number greater
than 6 but less than or equal
to 14.
5. Getting a perfect square.
A = {6, 12}
B = {2, 4, 6, 8, 10}
C = {4, 8, 12, 16}
D = {8, 10, 12, 14, 16}
E = {4, 16}

4. Each
outcome or
element of
the sample
space is
called a
__________.
TREE
DIAGRAM
It is a result
or a
consequence
. ___________
OUTCOME
OF AN
EVENT
It is a
subset of
a sample
space.
_________
EXPERI-
MENT
It is a set of
possible
outcomes
for a given
experiment
.
___________
SAMPLE
POINT
It is a
graphical
representation
used to list all
the
possibilities of
a sequence of
operations in
an
experiment.
____________
SAMPLE
SPACE
It is any
process or
study that
results in the
collection of
data, the
consequence
of which is
unknown or
uncertain.
______
EVENT
Sample
Point
P
Outcome of
an
experiment
RO
Event
BA
Sample
Space
BI
Tree
Diagram
LI
Experiment
TY

5. Should I bring
my umbrella
tomorrow?
How likely is it
that I will be
called in our
math class
today?
What are my
chances of getting
the correct answer
in a True/False
type?
Will I
probably win
in this game?

6.  How do you deal with these questions?
 Were you able to answer them with certainty?

7.  The branch of mathematics that deals with
uncertainty is
When we say PROBABILITY, we talk about

8.  PROBABILITY is a measure or estimation of how likely
it is that an event will occur. Activities such as tossing
or flipping a coin or picking a card from a standard
deck of cards without looking which could be repeated
over and over again and which have well – defined
results are called

9.  The results are called

10. WHAT IS THE
PROBABILITY?

11. Given: Set R = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
COLUMN A COLUMN B
The probability of having:
1. a 10
2. a 13
3. odd numbers
4. a number greater than 7
5. an odd numbers divisible by 3
6. a number divisible by 3
A. or
B.
C. Or or
D.
E.
F. or 0
G. or
D
F
G
E
C
A

12.  What formula can be used?

13.  The probability of any event is a number
(either a fraction, a decimal or a percent)
from 0 to 1.
 If an event will never happen,
then its probability is 0.

14.  If an event is sure to happen, then the probability is 1.

15.  One card is drawn from a well-shuffled deck of 52
cards. What is the probability of drawing…
 P(ace) =
 P(a red 10) =
 P(face card – K, J, Q) =
 P(NOT a diamond) =
4/52 or 1/13
2/52 or 1/13
12/52 or 3/13
39/52 or 3/4

16.  an EVEN number?
a PRIME number?
a multiple of 3?
9?
1-8?
4/8 or 1/2
4/8 or 1/2
2/8 or 1/4
0/8 or 0
8/8 or 1

17.  Find the probability of an event. Every answer, there is a corresponding
words and numbers that you need to arranged to reveal the quote.
 A. One of these names is to be drawn from a hat. Determine each
probability below:
Mary Jenny Bob Marilyn Bill Jack Jerry Tina Connie Joe
1. P(3-letter name) =
2. P(4-letter name) =
3. P(name with repeating letter) =
4. P(7-letter name) =
5. P(name starting with S) =
6. P(name ending with Y) =
0/10 or 0 - done
5/10 or ½ - Life
4/10 or 2/5 - decisions
3/10 - of
2/10 or 1/5 - Oftentimes
1/10 – has a lot

18.  B. One of these cards will be drawn without looking.
7. P(2) =
8. P(number divisible by 5) =
9. P(J) =
10. P(a number) =
12. P(T) =
13. P(a letter) =
J5
9S
M
104
2 J 7
4 10
8/12 or 2/3 - under
0/12 or 0 - are
2/12 or 1/6 - conditions
4/12 or 1/3 - uncertainties
3/12 or ¼ - in
1/12 - our

19. 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
2/10 or 1/5 - Oftentimes
4/10 or 2/5 - decisions
5/10 or ½ - Life
1/10 – has a lot
0/10 or 0 - done
3/10 - of
1/12 - our
3/12 or ¼ - in
2/12 or 1/6 - conditions
8/12 or 2/3 - under
0/12 or 0 - are
4/12 or 1/3 - uncertainties

20. LIFE HAS A LOT OF UNCERTAINTIES.
OFTENTIMES, OUR DECISIONS IN LIFE ARE
DONE UNDER
CONDITIONS OF UNCERTAINTY.
3 4 6 12
1 7 2 8 11
5 10
9 6

21.  Life has a lot of uncertainties. Oftentimes, our
decisions in life are done under conditions of
uncertainty. These are the probabilities of life.

22.  Suppose someone very dear to you was
diagnosed of having a serious illness.
According to the doctor, the illness can be
treated through an expensive operation
with a 50-50 chance of surviving. As a
person very close to the patient, will you
take the chance? Why? Why not?

23.  There are 3 C’s in life: Choice, Chance and Change. We
must make a CHOICE, to take the CHANCE, or our life
will never CHANGE.

25. TRY THESE:
Answer the following questions. Write it in ½
crosswise sheet of paper.
A large urn contains 15 billiard balls which are
numbered from 1 to 15. A ball is drawn at random and
the number is recorded. Find the probability p that the
number is:
 odd
 greater than 5
 even and less than 7
 even or less than 7