# HW 1 - Homework Set#1 Solutions IE 336 Spring 2011 1 Let S...

This preview shows pages 1–2. Sign up to view the full content.

IE 336 Spring 2011 1. Let S denote the sample space. If events B i partition the sample space, then: S = B 1 B 2 ∪ ··· ∪ B n If A is an event from the sample space, then A can also be expressed as: A = A S = A ( B 1 B 2 ∪ ··· ∪ B n ) = ( A B 1 ) ( A B 2 ) ∪ ··· ∪ ( A B n ) Using axiom 3: P ( A ) = P ( A B 1 ) + P ( A B 2 ) + ··· + P ( A B n ) (1) Recall the deﬁnition of conditional probability: P ( A B i ) = P ( B i ) P ( A | B i ) (2) Substituting (2) into (1): P ( A ) = P ( B 1 ) P ( A | B 1 ) + P ( B 2 ) P ( A | B 2 ) + ··· + P ( B n ) P ( A | B n ) P ( A ) = n X i =1 P ( B i ) P ( A | B i ) 2. (a) A= { 1, 2, 3, 4, 5, 6 } , B = { 1, 3, 5, 11, 13, 15, 17,19, 21 } , C = { 6, 14, 22 } (b) If two events are independent, then P ( A B ) = P ( A ) P ( B ). A B = { 1 , 3 , 5 } , so P ( A B ) = 3 18 = 1 6 . Checking independence: P ( A ) · P ( B ) = 6 18 · 9 18 = 1 6 = P ( A B

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/05/2011 for the course IE 336 taught by Professor Bruce,s during the Spring '08 term at Purdue.

### Page1 / 3

HW 1 - Homework Set#1 Solutions IE 336 Spring 2011 1 Let S...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online