Grade 9 – Unit 24
Probability
Introduction
What is Probability?
The possibility of an even occurrence is called Probability.
In grade 8 you have learned there are two types of probabilities.
Experimental Probability
Theoretical probability
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Introduction
In day-to-day life when we observer the things happen in the
environment or in the world can be categorized into 3 ways.
Possible Events – Exactly happens in real life
Eg: Sun rises from east
Probable Events – Cannot predict priorly / May or may not
happen
Eg: Today is Raining
Impossible Events – Events that are never happens
Eg: A chicken lay an egg.
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Experimental Probability
• Finding the probability by performing an action or an experiment is
called experimental probability.
• Experimental probability find using the fraction of Success or
success fraction of the event.
• Success fraction mean the the ratio between the outcome against
the Total number of experiments.
Eg: if you tossed a coin 50 times and you obtain 28 times of
head, then the success fraction of obtain head is,
𝑁𝑜 𝑜𝑓 𝐻𝑒𝑎𝑑𝑠 𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑 28 14
𝑆𝑢𝑐𝑐𝑒𝑠𝑠 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = = =
𝑁𝑜 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑐𝑜𝑖𝑛 𝑡𝑜𝑠𝑠𝑒𝑑 50 25
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Theoretical Probability
• Finding the probability using the behaviour of the given values are
called Theoretical probability.
• Theoretical probability find using the possibility values.
Eg: if a bag contains 5 black pebbles, 4 red pebbles and 6 white
pebbles, then the probability of drown a white pebble is,
𝑁𝑜 𝑜𝑓 𝑤ℎ𝑖𝑡𝑒 𝑃𝑒𝑏𝑏𝑙𝑒𝑠 6 2
𝑝(𝑊ℎ𝑖𝑡𝑒 𝑃𝑒𝑏𝑏𝑙𝑒) = = =
𝑇𝑜𝑡𝑎𝑙 𝑃𝑒𝑏𝑏𝑙𝑒𝑠 15 5
• 𝑝(𝑊ℎ𝑖𝑡𝑒 𝑃𝑒𝑏𝑏𝑙𝑒) means The probability of obtained white pebbles. 𝑝
refers for 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦.
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Random Experiment
• An experiment performs without knowing the outcome priorly is
called random experiment.
• Experiment always performs to find the output of that event.
• Therefore, to define an random experiment, you have to know
characteristics of random events.
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Characteristics of a Random Event
• Event can be occurred repeated any number of times.
Eg: Toss an unbiased coin 50 times
• All possible outcomes are priorly known (before Experiment).
Eg: Head and Tail will be the outcome
• Cannot be state the certainty of an outcome in a specific .
Eg: 37th toss outcome will be head
• If Experiment is repeated, No pattern can recognize.
Eg: first 3 heads next 2 tail again next 3 heads and nest 2 is tail
likewise
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Sample Space
• The all-possible outcomes of a random experiment defines as
Sample Space.
• This is denoted as 𝑆.
• All possible outcomes can represent as set notation.
Eg: Rolling a fair die
The all-possible outcomes are 1, 2, 3, 4, 5 and 6. Therefore,
𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔}
𝒏 𝑺 =𝟔
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Equally Likely Event
• If a random experiment produced all outcomes have even
opportunities to be obtained is called equally likely event.
• The object used to perform equally likely event is called fair or
unbiased object.
Eg: When you toss a coin, heads and tails both can obtained, and
the number of outcomes are equal in any random experiment then
the coin is called fair coin.
Out of 50 attempts, 27 are heads & 23 are tails they are equally likely
events. But 12 heads & 38 tails are not equally likely events.
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Probability of an Event
• Consider if the specific or expected outcome of an event is 𝐴 and
the total outcome of the same event is 𝑆, then the Probability of the
specific or expected event denoted as,
𝑁𝑜 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡 =
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑛(𝐴)
𝑝 𝐴 =
𝑛(𝑆)
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Exercise
24.4
Example
(i) 𝑆 = {𝐴, 𝐵, 𝐶, 𝐷, 𝐸, 𝐹, 𝐺, 𝐻}
𝑛(𝐵) 1
(ii) 𝑝 𝐵 = =
𝑛(𝑆) 8
𝑛(𝑉) 2 1
(iii) 𝑉 = 𝐴, 𝐸 𝑛 𝑉 =2 𝑝 𝑉 = = =
𝑛(𝑆) 8 4
𝑛(𝐾) 0
(iv) 𝑛 𝐾 = 0 𝑝 𝐾 = = =0
𝑛(𝑆) 8
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Exercise
24.4
Example
𝑆 = 1,2,3,4,5 𝑛 𝑆 =5 (ii) No of incorrect Answers = 4
(i) No of Correct Answers = 1 𝑛(𝑖𝑛𝑐𝑜𝑟𝑟𝑒𝑐𝑡) 4
𝑝 𝑖𝑛𝑐𝑜𝑟𝑟𝑒𝑐𝑡 = =
𝑛(𝑆) 5
𝑛(𝐶𝑜𝑟𝑟𝑒𝑐𝑡) 1
𝑝 𝐶𝑜𝑟𝑟𝑒𝑐𝑡 = =
𝑛(𝑆) 5
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
Summary
• Probability means the possibility of an event occur.
• Random experiment consider four characteristics during an event
occur.
• All possible outcomes of an event is called Sample space.
• If a random experiment produced all outcomes have even
opportunities to be obtained is called equally likely event.
• Probability of an event can be denoted as,
𝑁𝑜 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡 =
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑛(𝐴)
𝑝 𝐴 =
𝑛(𝑆)
R Chrysanthus Perera| MEd, PGDIT, BAPSY, HDIT, DIT, DCETT, DELM, Dip in Math
