Strategic Intervention Material on Basic Probability

1. Basic
Probability

2. OBJECTIVES
 Define experiment, outcome, sample space,
and event.
 Explain and interpret the probability of an
event.
 Count the number of occurrences of an
outcome in an experiment
 Solve simple problems involving probabilities
GUIDE CARD

3. What is
Probability?
Probability is a
measure of how
likely an event is to
occur.

4. What is
Probability?
For example –
• Today there is a
60% chance of rain.
• The odds of
winning the lottery
are a million to one.
What are some
examples you can
think of?

5. How do we
write
Probabilities?
Fractions from 0 to 1
Decimals from 0 to 1
Percents from 0% to
100%
Impossible Unlikely Equal Chances Likely Certain
0 0.5 1
0% 50% 100%
½

6. PROBABILITY
• IF AN EVENT IS CERTAIN TO HAPPEN,
THEN THE PROBABILITY OF THE EVENT IS
1 OR 100%.
• IF AN EVENT WILL NEVER HAPPEN, THEN
THE PROBABILITY OF THE EVENT IS 0 OR
0%.
• IF AN EVENT IS JUST AS LIKELY TO
HAPPEN AS TO NOT HAPPEN, THEN THE
PROBABILITY OF THE EVENT IS ½, 0.5 OR

7. • AN OUTCOME IS THE RESULT OF A SINGLE
TRIAL OF AN EXPERIMENT
• WHEN ROLLING A NUMBER CUBE,
THE POSSIBLE OUTCOMES ARE 1,
2, 3, 4, 5, AND 6

8. EXAMPLE
•THE DIE TOSS:
•SIMPLE EVENTS: SAMPLE
SPACE:1
2
3
4
5
6
E1
E2
E3
E4
E5
E6
S ={E1, E2, E3, E4, E5,
E6} S
•E1
•E6
•E2
•E3
•E4
•E5

9. • AN EVENT IS A SPECIFIC RESULT OF A
PROBABILITY EXPERIMENT
• WHEN TOSSING A DICE, THE EVENT OF
ROLLING AN ODD NUMBER IS 3 (YOU COULD
ROLL A 1, 3 OR 5).
• WHEN ROLLING A DICE, THE EVENT OF
ROLLING A NUMBER GREATER THAN 2 ( YOU
COULD ROLL 3,4,5 OR 6)

10. •The die toss:
–A: an odd
number
–B: a number > 2
S
A ={E1, E3, E5}
B ={E3, E4, E5, E6}
B
A
•E1
•E6
•E2
•E3
•E4
•E5

11. • THE PROBABILITY OF AN EVENT IS
WRITTEN:
P(EVENT) = NUMBER OF WAYS EVENT CAN
OCCUR
TOTAL NUMBER OF OUTCOMES

12. P(EVENT) = NUMBER OF WAYS EVENT CAN
OCCUR
TOTAL NUMBER OF OUTCOMES
WHAT IS THE PROBABILITY OF GETTING HEADS
WHEN FLIPPING A COIN?
P(HEADS) = NUMBER OF WAYS = 1 HEAD ON A COIN = 1
TOTAL OUTCOMES = 2 SIDES TO A COIN
= 2
P(HEADS)= ½ = 0.5 = 50%

13. EXAMPLES
1. What is the probability of rolling an odd
number when tossing a number cube?
STEPS.
A. When rolling a number cube, the possible
outcomes are 1, 2, 3, 4, 5, and 6
no. of possible outcomes = 6
B. When tossing a number cube, the event of
rolling an odd number is 3 (you could roll a 1, 3
or 5).
no. of ways an event can occur = 3
C. P(odd ) = no. of ways an event can occur = 3
no. of possible outcome = 6
P( odd) =
3
6
𝑜𝑟
1
2

14. 1. What is the probability that the spinner
will stop on part A?
2. What is the probability that the
spinner will stop on
(a) An even number?
(b) An odd number?
3. What is the probability that the
spinner will stop in the area
marked A?
AB
C D
3 1
2
A
C B
ACTIVITY CARD # 1

15. EXAMPLES
2. What is the probability of rolling a number
greater than 2 when tossing a number cube?
STEPS.
A. When rolling a number cube, the possible
outcomes are 1, 2, 3, 4, 5, and 6
no. of possible outcomes = 6
B. When tossing a number cube, the event of
rolling an odd number is 4 (you could roll a 3,
4, 5 or 6).
no. of ways an event can occur = 4
C. P(odd ) = no. of ways an event can occur = 4
no. of possible outcome = 6
P( odd) =
4
6
𝑜𝑟
2
3

16. 1. What is the probability of spinning a
number greater than 1?
2. What is the probability that a spinner
with five congruent sections numbered
1-5 will stop on an even number?
3. What is the probability of rolling a
multiple of 2 with one toss of a dice ?
ACTIVITY CARD # 2
21
3 4

17. – Suppose that 10% of the U.S.
population has red hair. Then for a
person selected at random,
FINDING PROBABILITIES
•PROBABILITIES CAN BE FOUND
USING
• ESTIMATES FROM EMPIRICAL
STUDIES
• COMMON SENSE ESTIMATES BASED
ON EQUALLY LIKELY EVENTS.
P(Head) = 1/2
P(Red hair) =
.10
• Examples:
–Toss a fair coin.

18. EXAMPLE 1
TOSS A FAIR COIN TWICE. WHAT IS THE
PROBABILITY OF OBSERVING AT LEAST ONE
HEAD?
H
1st Coin 2nd Coin Ei
P(Ei)
H
T
T
H
T
HH
HT
TH
TT
1/4
1/4
1/4
1/4
P(at least 1 head)
= P(E1) + P(E2) + P(E3)
= 1/4 + 1/4 + 1/4 =
3/4

19. EXAMPLE 2
A BOWL CONTAINS THREE M&MS®, ONE
RED, ONE BLUE AND ONE GREEN. A CHILD
SELECTS TWO M&MS AT RANDOM. WHAT
IS THE PROBABILITY THAT AT LEAST ONE
IS RED?
st M&M 2nd M&M Ei P(Ei)
RB
RG
BR
BG
1/6
1/6
1/6
1/6
1/6
1/6
P(at least 1 red)
= P(RB) + P(BR)+ P(RG) +
P(GR)
= 4/6 = 2/3
m
m
m
m
m
m
m
m
m
GB
GR

20. ACTIVITY CARD # 3
The sample space of throwing a pair of
dice is

21. ACTIVITY CARD # 3
EVENT SIMPLE EVENTS PROBABILITY
Dice add to 3
Dice add to 6
Red die show 1
Green die show 1
(1,2),(2,1)
(1,5),(2,4),(3,3),
(4,2),(5,1)
(1,1),(1,2),(1,3),
(1,4),(1,5),(1,6)
(1,1),(2,1),(3,1),
(4,1),(5,1),(6,1)
2/36
5/36
6/36
6/36

22. PROBABILITY WORD PROBLEM:
• LAWRENCE IS THE CAPTAIN OF HIS TRACK TEAM. THE
TEAM IS DECIDING ON A COLOR AND ALL EIGHT
MEMBERS WROTE THEIR CHOICE DOWN ON EQUAL SIZE
CARDS. IF LAWRENCE PICKS ONE CARD AT RANDOM,
WHAT IS THE PROBABILITY THAT HE WILL PICK BLUE?
NUMBER OF BLUES = 3
TOTAL CARDS = 8
yellow
red
blue blue
blue
green black
black
3/8 or 0.375 or 37.5%

23. • DONALD IS ROLLING A NUMBER CUBE LABELED 1 TO
6. WHAT IS THE PROBABILITY OF THE FOLLOWING?
A.) AN ODD NUMBER
ODD NUMBERS – 1, 3, 5
TOTAL NUMBERS – 1, 2, 3, 4, 5, 6
B.) A NUMBER GREATER THAN 5
NUMBERS GREATER – 6
TOTAL NUMBERS – 1, 2, 3, 4, 5, 6
LET’S WORK THESE TOGETHER
3/6 = ½ = 0.5 = 50%
1/6 = 0.166 = 16.6%

24. ASSESSMENT CARD
1. A coin in tossed thrice. What is the probability of
having two head and a tail?
2. A die is rolled. What is the probability of rolling a
number that is greater than 6?
3. A glass jar contains 80 red, orange, yellow and green
plastic chips. If the probability of drawing a random a
single ORANGE chips is 1/8 , how many ORANGE
chips is on the glass jar?
4. Jun rolls two dice. The first die show a 2. The second
die rolls under his desk and he cannot see it. What is
the probability that both dice shows 2?
5. In 2000 ticket draw for an educational prize, your
name was written on 58 tickets. What is the
probability that you will get the prize?

25. ANSWER KEY
Activity #1
1.
1
4
2.
a)
1
3
b)
2
3
3.
1
3
Activity # 2
1.
3
4
2.
2
5
3.
1
2
Assessement
1.
3
8
4.
1
6
2. 0 5.
58
2000
𝑜𝑟 0.029
3. 10
Event Simple events Probability
Dice add to 3 (1,2),(2,1) 2
36
𝑜𝑟
1
18
Dice add to 6 (1,5),(2,4),(3,3),
(4,2),(5,1)
5
36
Red die show 1 (1,1),(1,2),(1,3),
(1,4),(1,5),(1,6)
6
36
or
1
6
Green die show 1 (1,1),(2,1),(3,1),
(4,1),(5,1),(6,1)
6
36
or
1
6
ACTIVITY # 3

26. ENRICHMENT CARD
1. How many 3-digit lock combinations can
we make from the numbers 1, 2, 3, and 4?
2. A lock consists of five parts and can be
assembled in any order. A quality control
engineer wants to test each order for
efficiency of assembly. How many orders
are there?
3. Three members of a 5-person committee
must be chosen to form a subcommittee.
How many different subcommittees could
be formed?
4. A box contains six M&Ms®, four red and

27. REFERENCE CARD
• Learner’s Material – Mathematics VIII, First Edition
2013 pp. 557- 580
• Teachers Guide– Mathematics VIII, First Edition
2013 pp. 595- 637
• http://www.pstat.ucsb.edu/faculty/yuedong/5E/
5Enote5.ppt
• http://www.cobblearning.net/aimeetait/files/201
5/07/Simple-Probability-2hrtetn.ppt