# 2.07B - ection 7B Independence 1 2 Formally we define two...

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

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.

Unformatted text preview: ection 7B, Independence 02/02/2010 1 2 Formally, we define two events A and B to be independent if any of the following is true: (Stochastically) Independent Events Intuitively, two events A and B are independent events if knowledge of the occurrence of one of them does not affect the likelihood that the other occurs. Two events which are not independent are called dependent . ⎩ ⎨ ⎧ > > ← ⎭ ⎬ ⎫ = = ← = ∩ ) ( in ) ( ); ( in ) ( : provided theorem, a by , definition the to equivalent ) ( ) ( ) ( ) ( ) ( ) ( independence of definition the ) ( ) ( ) ( ) ( c A P b B P B P A B P c A P B A P b B P A P B A P a 3 Example . A bowl contains 7 blue chips and 3 red chips . Two chips are drawn at random, in order and with replacement . Let S = set of all ordered pairs of distinct chips, A be the event that the first chip drawn is red , and B be the event that the second chip drawn is blue . Are the events A and B independent? Solution 1 : A ∩ B = event first is red and second is blue . 3 ⋅ 10 = 30 3 ⋅ 7 = 21 10 ⋅ 10 = 100 | S | = | A | = | B | = | A ∩ B | = 10 ⋅ 7 = 70 P ( A ) = P ( B ) = P ( A ∩ B) = P ( A ) P ( B ) = P ( A ) = 30/100 = 0.3 P ( B ) = 70/100 = 0.7 P ( A ∩ B) = 21/100 = 0.21 P ( A ) P ( B ) = (0.3)( 0.7) = 0.21 P ( A ) = 30/100 = 0.3 P ( B ) = 70/100 = 0.7 P ( A ∩ B) = 21/100 = 0.21 P ( A ) P ( B ) = P ( A ) = 30/100 = 0.3 P ( B...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

2.07B - ection 7B Independence 1 2 Formally we define two...

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

View Full Document
Ask a homework question - tutors are online