General
UNIT 18:Introduction to Probability
Key unit competence
By the end of this unit, a learner should be able to play games based on the
probability.
Attitudes and values
Appreciate the importance of following rules and taking turns when playing
games of cards and coins, throwing dice, snakes and ladders and bingo with
probability.
Meaning of Probability
Probability is a branch of Mathematics which deals with the possibility of
something happening. The possibility of something happening is also called
the chance or likelihood of something happening.
Games such as tossing a coin, cards, throwing dice, snakes and ladders andbingo etc. are played based on probability.
Activity 18.1
Tossing a coin
• Pair up with one of your classmates.
• Together with your friend, you will decide which side of
the coin is the head and which one is the tail. Confirmwith the teacher which side is the head (H) or tail (T).
• Each one of you will draw a table like the one shown below in your book.
• You will toss the coin, allow it to fall on the floor and note the side facing
up. If the head is facing up in the 1st toss, then write H in the table.
Otherwise, write T for a tail facing up.
• Repeat the experiment 9 more times and record your results as honestly
as possible in the table.
• Let your friend also repeat what you have done and help him/her record
his/her results in a table.• Compare your results and see who has more heads than the other.
Activity 18.2
Tossing 3 coins at once
• In this activity, you will pair up with a
classmate.
• Carefully observe the coin faces and
decide which the heads are.
• You will be required to toss all the three coins at the same time and
note the sides of the coin facing up. It is good to decide on a winning
combination before starting the game. For instance, the winning
combination may be getting 2 heads and 1 tail (HHT). If you get anything
else, then you have lost.
• Toss the three coins at once and note the sides facing up. Record your
result as a win or a loss.
• Give the three coins to your friend and let him/her toss.• Repeat the experiment several times and see who gets 10 wins first.
Activity 18.3
In this class activity, you will play a game of cards and discover how lucky you
are!!!!
(a) Open the pack of playing cards. Count the total number of cards and
record your answer.
(b) Group the cards of the same type together. You should have 5 groups of
cards namely; hearts, spades, clubs, diamonds and jokers.
(c) Count and record the number of each suit of cards.
(d) How many picture cards are there altogether?
(e) Shuffle the pack of playing cards very well. Deal 5 cards to your neighbour.
(f) Open the cards so that everybody can see. Count the number of aces he/
she has got and record the number down.
(g) Repeat the shuffling and dealing for everybody in the group.Play the game for a number of times, each time recording the number of
aces each pupil has got.
(i) The pupil who gets 10 aces first is the winner of this game.
(j) Is the game fair? If you think it is unfair, discuss how you could make itfair for everyone.
Assessment Exercise
1. Discuss the following questions: (Refer Activity 18.1)
(a) Was the game fair?
(b) Are there some winning strategies for getting a head up?
(c) Some people believe that girls will get more “heads” up than
“tails”. Do you agree?
(d) Some people think that tossing the coin first makes you get “tails”
only. Is this true?
2. Discuss the following questions: (Refer Activity 18.2)
(a) Were we very sincere while doing the experiment?
(b) Is it possible to get 2 heads and a tail?
(c) Some people believe that small coins show heads only and bigcoins show tails only. Do you agree with this?
Internet Resource
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GLOSSARY
Abacus: a table or frame used
for performing arithmetical calculations.
Acre: a unit of land measure equivalent to 4046 square metres.
Addends: the numbers being added together.
Angle: circular measure of the space between two intersecting lines.
Acute angle: Angle less than 90˚.
A.M. : Ante Meridian, time before midday.
Architect: Stet person who designs and constructs buildings.
Area: measure of the 2D space surrounded by lines.
Arithmagon: a polygon with numbers at its vertices which determine
the numbers written on its edges.
Arithmetic: branch of mathematics that deals with calculations.
Calculator: instrument used to help adding, subtracting, multiplying and
dividing numbers.
Calendar: an arrangement of dates, days and months of the year.
Capacity: the amount of liquid a given container can carry.
Circle: closed figure with all points at equal distance from the centre.
Circumference: distance around a circle.
Cube: closed figure with six equal faces.
Coin: metallic money in the form of a small disc.
Compass: device for telling the direction.
Data: any information collected for statistics.
Denominator: the lower number in a fraction.
Diagonal: a line (which is not a side)
joining any two vertices of a polygon.
Diameter: distance from one point on a circumference to the other
through the centre. It is twice the radius of a circle.
Digit: a numeral or number.
Edge: the boundary line of a surface.
Even number: a number which is divisible by 2.
Equivalent fractions: two fractions
which have the same numerical value.
Estimate: to approximate something.
Face: any of the flat surface of a solid figure.
Factors: any two numbers multiplied together to form another number.
Fraction: ratio of two numbers; the numerator and the denominator.
Gram: a unit of mass equivalent to 0.001 kg.
Graph: a diagram displaying data showing the relation between two
quantities.
G.C.F. : Greatest Common Factor.
H.C.F. : Highest Common Factor.
Intersect: for lines, to meet at a point.
L.C.M.: Lowest Common Multiple.
Line: a straight path through two or
more points.
Litre: the unit of capacity equivalent to 1000 cm3.
Multiple: a number that may be divided by another number with
no remainder.
Numerator: the lower number of a fraction.
Oblique line: a line which is neither horizontal nor vertical. It is a
sloping/slanting line.
Pair of compasses: a tool consisting of two arms used to draw circles.
Parallel lines: these are lines which do not meet at all.
Pentagon: a 5-sided closed figure.
Perimeter: the distance around a given figure
Perpendicular lines: two or more lines which intersect at an angle
of 90°.
Plane: a flat surface.
Point: a small dot used to represent the location of something.
Polygon: a closed figure bounded by straight or curved edges.
Prime number: a number with only two factors. One factor being 1
and the other one is itself.
Probability: this is the chance or likelihood of something happening.
Protractor: This is a geometrical instrument used for measuring angles.
Quadrilateral: This is any 4-sided closed figure.
Radius: this is the distance from the centre of a circle to any point on
the circumference of the circle. It is half the diameter.
Range: this is the difference between the largest and smallest numbers
in a data.
Ratio: it refers to the division of two numbers.
Remainder: a number which is left when two numbers are divided.
Right angle: an angle which is equal to 90°.
Square: a closed 4-sided figure with all sides equal.
Symmetrical shape: a shape that can be separated into two exactly
equal parts which can overlap.
Tossing a coin: throwing a coin in air so that it falls with one side facing upwards.
Triangle: a closed figure with three sides, three angles and three vertices.
Vertex: a point on a polygon where two lines meet.
Volume: the space occupied by an object.
X-axis: the horizontal line on the Cartesian plane.
Y-axis: the vertical line on the Cartesian plane