Lecture 1&2: Probability

Probability is a study of random events and chances. The modern theory of probability is founded by two mathematicians, Pascal and Fermat during the seventeenth century and it was started by the study of the chance of winning in a gambler's game.

In these two lectures, you need to understand the first few concepts.

1. The meaning of the basic terms: experiment, outcome, sample space and event

2. Classical method of obtaining probability (Important concept!!!): the probability of an event equals to the no. of ways that the event can occur dividing the total number of possible outcomes.

Remark: Classical method is useful only if each outcome are equally likely to happen.

3. Venn Diagram: Learn how to draw the Venn diagram and derive the formula from the Venn diagram

4. Conditional probability (Extremely important!!!):

• Definition: P(A|B)=P(A intersect B)/P(B)
• To calculate conditional probability, please make use of the definition rather than depending on your intuition. Your intuition is not always correct!

Tips for questions on probability:

• identity and define the events first
• change all the statements in terms of probability
• summarize the information in the question before you start to do the question

You can attempt all the questions in tutorial 13 except Q3 and 4.