Ch.8 Introduction to probability
References
Cambridge IGCSE Mathematics core and extended course book by Karen Morrison and Nick Hamshew
DT
Sub Topic(s) -
Basic probability
Theoretical probability
The probability that an event does not happen
Learning objective:
At the end of the lesson learner’s will be able to -
express the probability mathematically
calculate probabilities associated with simple experiments
calculate theoretical probability
calculate the probability of an event not occurring
Go through the following slide and try to answer the scenario based questions.
Try to answer the following questions-
● What kind of weather is today? What are the chances of weather remaining the same tomorrow?
● In a cricket match between India and Australia, which team do you think is likely to win?
● Suppose our school plans for one day picnic, what are the chances of your parents giving permission for the same?
● Can we say that these questions show uncertainty of things to happen?
● Can we measure this uncertainty?
Points to remember -
calculation done to measure the uncertainty of a situation to occur or not is called probability.
It is a numerical value given to the chance of the occurrence of a certain situation.
Go through the following slides to understand the different terms used in probability, formula for calculating probability of any event, concept of theoretical and experimental probability and concept of probability of event not occuring.
Watch the following video to understand the concept of probability scale
Solve/Revise Exercise - 8.1
Sub Topic(s) -
Relative frequency as an estimate of probability
Possibility diagram
Learning objective:
At the end of the lesson learner’s will be able to -
use possibility diagram to calculate probability
understand relative frequency as an estimate of probability calculate theoretical probability
Points to remember -
When an experiment is repeated many times we can use the relative frequency as an estimate of the probability of the event occurring.
Relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted.
Relative frequency is used in probability when it is not easy to evaluate the probability of certain events by looking at their situations.
For example the result of any match for win, lose or tie cannot be determined as all outcomes are equally likely, but one can estimate the probability by looking at the previous win or lose of matches and also the way the game is proceeding so far.
Relative frequency = number of successful trials/total number of trials
Watch the following video to know the basic concept of relative frequency with example.
Go through the following slides to understand the concept of relative frequency with example.
Watch the following video to understand the basic concept of possibility diagram with an example.
Go through the following slide to understand the basic concept of possibility diagram.
Solve/Revise Exercise - 8.2
Solve all the questions from Worksheet 1 and Worksheet 2 based on basic of probability and relative frequency.
WS_ 1_QP_Cambridge_IX_Math_Introduction to Probability.pdfWS_2 _QP_Cambridge_IX_Math_Introduction to Probability.pdfSub Topic(s) -
Combined events
Combining independent and mutually exclusive events
Learning objective:
At the end of the lesson learner’s will be able to -
calculate probability of combined events
identify when the events are independent and when the events are mutually exclusive
Exclusive events
· Two events are mutually exclusive if they cannot occur at the same time. For example selecting an even number or selecting a ‘one’ from a set of numbers
· The ‘OR’ Rule
· For exclusive events A and B
· p( A or B) = p(A) + p(B)
Example: One ball is selected at random from a bag containing 5 red balls, 2 yellow balls and 4 white balls.
Find the probability of selecting a red ball or a white ball. Solution: The two events are exclusive.
p(red ball or white ball) = p(red) + p (white)
= 5/11+ 4/11 = 9/11
Independent Events
· Two events are independent if the occurrence of one event is unaffected by the occurrence of the other.
· For e.g. Obtaining a ‘head’ on one coin, and a ‘tail’ on another coin when the coins are tossed at the same time.
· The ‘AND’ rule:
· p(A and B) = p(A) × p(B)
Example: A fair coin is tossed and a fair die is rolled. Find the probability of obtaining a ‘head’ and a ‘six’.
Solution: The two events are independent.
p(head and six) = p(head) × p(six)
= 1/2* 1/6 = 1/12
Watch the following video to understand the concept of independent and mutually exclusive events with an example.
Solve/Revise Exercise - 8.3
Solve all the questions from Worksheet 3 based on possibility diagram, combining events and combining independent and mutually exclusive events.
WS_3_ QP_Cambridge_IX_Math_Introduction to Probability.pdfAT