Chapter 2. Combinatorial Probability

Chapter 2. Combinatorial Probability - § 2 Combinatorial...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: § 2 Combinatorial probability § 2.1 Definitions 2.1.1 Definition. Consider an experiment with a finite number of different possible outcomes. The set Ω of all possible outcomes is called the sample space . 2.1.2 An event A is a subset of Ω. It occurs if and only if the outcome of the experiment belongs to the subset A . 2.1.3 Definition. Assume that each outcome in Ω has EQUAL chance of occurring. The probability of event A is defined by P ( A ) = no. of outcomes in A no. of outcomes in Ω . 2.1.4 Example. If we roll a dice, possible outcomes are Ω = { 1 , 2 , 3 , 4 , 5 , 6 } . That “an even score turns up” is the event A = { 2 , 4 , 6 } . The probability of getting an even score is P ( A ) = 3 6 = 1 2 . 2.1.5 In the above definition, it is important that all outcomes in Ω must be equally likely, such that for each ω ∈ Ω, P ( { ω } ) = 1 no. of outcomes in Ω . Counter-example. When we toss a coin, it can land on a head, a tail OR on its edge. We may define Ω = { H , T , Edge } . The above definition instructs that P ( { H } ) = P ( { T } ) = P ( { Edge } ) = 1 / 3 , which is clearly not sensible. § 2.2 Examples 2.2.1 If we roll 2 dice, what is the probability that the total is 6? Here Ω = { (1 , 1) , (1 , 2) ,..., (1 , 6) , (2 , 1) ,..., (6 , 6) } contains 6 × 6 = 36 outcomes. The event of interest is A = { (1 , 5) , (2 , 4) , (3 , 3) , (4 , 2) , (5 , 1) } , 8 which contains 5 outcomes. Thuswhich contains 5 outcomes....
View Full Document

This note was uploaded on 04/29/2010 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.

Page1 / 4

Chapter 2. Combinatorial Probability - § 2 Combinatorial...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online