
SIBC Radio Broadcasts
 8 May, 2020: Population and Urban Drift 1
 15 May, 2020: Population and Urban Drift 2
 22 May, 2020: Probability 1
 29 May, 2020: Probability 2
 5 June, 2020: Literature – Poetry 1
 12 Jun, 2020: Literature – Poetry 2
 19th June, 2020: Science – Genetics
 3rd July, 2020: Economics and Commerce
 10th July, 2020: Accounting
 17th July, 2020: Agriculture
 24th July, 2020: Animal Production
 24th August, 2020: New Testament Study
22 May, 2020: Probability 1
This is the third session of the Student Learning Continuity Program for Years 1012, an educational series made possible by the Ministry of Education and Human Resources Development (MEHRD).
Presenters: Lenny Olea and Martin Ruhasia
Topic: Probability
Note – For Year 12 (Form 6), your Mathematics Common Assessment Task (CAT) will be on Probability.
Objectives:
By the end of this session students should be able to
 Express probability in a variety of ways; as a percentage, a decimal, a fraction or a number out of a total
 Differentiate between equally likely and nonequally likely events
 Relate likeliness of an event to probability from 0 to 1
 Differentiate between mutually exclusive events and independent events
 Identify complementary events
 Use concepts of probability to determine the probability of events in situations where sample with and without replacement takes place.
 Represent the possible outcomes of an experiment on a tree diagram.
Introduction:
The concept of probability is part of our everyday lives. It is a household word. We hear it or speak it every day. Weather forecasts are given probabilistically. Most people know that probability is somehow connected with chances. In statements such as:
“It is likely to rain today”.
“I have a reasonable chance of passing this course”.
“He will probably win the tennis competition”.
“I am almost certain that he will be elected”.
We are referring to situations where there is an element of uncertainty about the outcome of a particular situation. In probability theory, we are concerned with assigning a “measure of likelihood” or “probability of occurrence” to the outcome of an experiment. Probability is the chance that a particular event will occur in a given set of circumstances, depending on the possible events.
Probability lies between 0 and 1. If the probability of an event is 0, we are certainly sure such event will not occur. If the probability of an event is 1, we are certainly sure such event will occur.
Let us look at some events and assign probabilities to it:
“What is the probability that ice will fall in Honiara next week?”
“What is the probability that it will rain tomorrow?”
“A teacher chooses a student at random from a class of 30 boys. What is the probability that the student chosen is a boy?”
We can estimate probabilities from experimental results by using the rule:
Sampling with replacement and without replacement
Sampling with replacement
Eg 1. From a wellshuffled deck of 52 cards one card is selected at random. Find the probability of selecting:
a). a heart b). a picture card c). a red card
Sampling without replacement
Eg2. A mixed team of five boys and four girls elects a captain and a vice captain.
a). Illustrate this with a tree diagram.
b). Find the probability of electing a boy captain and a girl vicecaptain.
c). Find the probability of electing the same sex captain and vicecaptain.
PROBABILITY OF TWO EVENTS
MUTUALLY EXCLUSIVE EVENTS
Mutually Exclusive Events:
 cannot happen at the one time
 have no element in common
Example
Consider when a die is rolled. Let A be the event that an even number turns up and B be the event that an odd number shows.
Sample Space = {1 , 2 , 3, 4, 5, 6 }
Events, A = { 2 , 4 , 6} and B = { 1 , 3 , 5 }
Events A and B have no element in common. An even and odd number cannot occur at the one time on a single toss of a die.
Therefore the events A and B are mutually exclusive.
NB: If events have no element in common, those events are called mutually exclusive events.
COMPLEMENTARY EVENTS
If A is any event in a sample space S and if A’ is the complement of A, then
P (A) + P (A’) = 1
P (A) = 1 – P (A’)
Consider when a die is rolled. Let A be the event that an even number turns up. The probability that an odd number shows up is
Sample Space = {1, 2, 3, 4, 5, 6}
Event A = {2, 4, 6}
INDEPENDENT EVENTS
Two events are called independent events if the outcome of one event has no effect on the outcome of the other.
Example
A coin is tossed and a die is rolled. Let A be the event that a HEAD shows on the coin and B be the event that a 4 turns up on the die.
Events A and B are independent because the outcome of a 4 does not depend on whether a head has shown on the die
Thank you every students for listening and we hope you grasp some important basic concepts on this topic (Probability) to take with you when you return to school.
Our next session with you will on normal distribution curve and we’ll also explaining What to do when you carry out your Mathematics statistics minor research Project chapter by chapter.
For your information:
Form 3, Form 5 and Form 6 Mathematics, we create an account (page) on Facebook for revisions. You can go to that page and post your Mathematics questions and we’ll give you the solution. We are offering you a free service to you do your revisions. All you need to do is to buy your data and use wisely for this purpose.
Once again thank you every good students out there and all best in your studies.
Our contacts: Lenny Olea – 8628229
Martin Ruhasia – 7716696
Stay safe and have a blessed weekend.