Topic 4 Probability Flashcards
At the end of this lesson, students will be able to 1. Define the terms: Experiment, Trial, Outcome, Sample point, Sample Space, Probability Space and Event. 2. Calculate the probability of a single event. 3. Define complementary events.
What are the common words that we use in our daily life?
Probability as a measure of chance
Many things we do in our daily lives have an element of chance or uncertainty. We often use words such as ‘likely’, ‘unlikely’, ‘impossible’ or ‘sure’ to describe the chance of something happening.
What does this terminology, “Experiment” mean for probability?
An operation or a process with a result whose occurrence depends on chance (that can be repeated as many times as required).
What does this terminology, “Trial” mean for probability?
Each performance of an experiment.
What does this terminology, “Outcome” mean for probability?
The result of any trial.
What does this terminology, “Sample point” mean for probability?
Each outcome of an experiment.
What does this terminology, “Sample space” mean for probability?
The set of all possible outcomes of an experiment. This is also known as the universal set.
What does this terminology, “Event” mean for probability?
Any subset of the sample space.
How do you represent probability? Explain each of the letters used.
Suppose we carry out an experiment and let S be the sample space of the experiment. We let n(S) be the number of equally likely outcomes in the sample space S and n(E) in the number of outcomes that are favourable to an event E, then the probability that event E occurs, is denoted by P(E)
P(E)= number of outcomes favouring E/total number of possible outcomes in S= n(E)/n(S)
For any event E, what is the range of values for probability?
For any event E, 0 is smaller or equal than P(E) and P(E) is smaller or equal to 1.
What does P(E)=1 means?
P(E)=1 if and only if E is a certain event. Example, it will definitely occur.
What does P(E)=0 means?
P(E)=0 if and only if E is an impossible event. Example, it will never occur.
What is the complementary event of E? And how can you find the complementary event?
The complementary event of E is E’ , which consists of all outcomes in S but not in E. Hence the sum of the probability of an event and its complement must be 1.
P(E’)=1-P(E)
Example: Find the probability of not getting a ‘3’ when a dice is thrown.
P(get ‘3’)=1/6
P(not get ‘3)=1-1/6=5/6
