SAJC 2021_Ch2 Probability_Teacher version

SAJC 2021 JC1 H1 Mathematics Chapter 2: Probability 1 Chapter 2 (Statistics): Probability (Teacher’s copy) Objectives At the end of the chapter, you should be able to (a) understand that the probability of an event measures how likely the event will occur (b) construct a table of outcomes to calculate probabilities, and understand that the total probability of all possible outcomes is equal to 1 (c) calculate probabilities using addition and multiplication principles (d) use a Venn diagram to interpret probabilities such as P( )A , P( )AB , P( )AB , P( | )AB (e) understand the meaning of mutually exclusive events, and recognize events that are, or are not, mutually exclusive through practical examples; and use the result P( ) P( ) P( )A B A B   where A and B are mutually exclusive (f) understand the meaning of independent events, and use the result P( ) P( )P( )A B A B , where A and B are independent. (g) construct a tree diagram and use it to interpret and calculate probabilities, including probabilities of combined events and conditional probabilities. Contents 2.1 Basic Rules and Definitions 2.1.1 Basic Definitions 2.1.2 Classical (Theoretical) Definition of Probability 2.1.3 Basic Probability Rules 2.2 Tools for Finding Probabilities 2.2.1 Venn Diagram 2.2.2 Tree Diagram 2.2.3 Table of Outcomes 2.3 Conditional Probability 2.4 Mutually Exclusive Events 2.5 Independent Events 2.6 A Mix of Probabilities "Life is a school of probability.” --Walter Bagehot

SAJC 2021 JC1 H1 Mathematics Chapter 2: Probability 2 2.1 Basic Rules and Definitions 2.1.1 Basic Definitions Definition Experiment 1 Experiment 2 An experiment or trial is a process that generates data. Throw a six-sided fair die. Toss a fair coin 2 times. An outcome is the result of a single trial of an experiment. Obtain a ‘2’ Obtain a ‘Head’, then a ‘Tail’ (HT) The sample space, S, of an experiment is the set of all possible outcomes. The number of outcomes in the sample space is denoted by n(S). {1, 2, 3, 4, 5, 6} n(S)= 6 {HH, HT, TH, TT} n(S)= 4 An event is a subset of the sample space. The number of outcomes in an event A is denoted by n(A). Let A be the event “a prime number is obtained”. A = {2, 3, 5} n(A)= 3 Let B be the event “2 heads is obtained”. B = {HH} n(B)= 1 Probability is the measure of how likely an event is to occur. AA S n( ) 3 1P( ) = = =n( ) 6 2 1 4 BB S n( )P( ) = =n( ) 2.1.2 Classical (Theoretical) Definition of Probability For equally likely outcomes from a finite sample space S, the probability of an event A is defined as P(A) Number of Ways Event can occur n( ) Total Number of Possible Outcomes n( ) AA S Example 1 A playing card is to be drawn at random from a pack of 52 cards. Find the probability that (i)