f2006lecNotesWeek08 - 22 Probability (cont.) 22.1...

Info iconThis preview shows pages 1–2. 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: 22 Probability (cont.) 22.1 Independent events: P ( A B ) = P ( A ) P ( B ) Epp 6.9 events A and B are independent iff P ( A B ) = P ( A ) P ( B ) an example consider 3-child families assign equal probabilities to GGG, GGB, ... , BBB (all 1 8 ) let A be: 1st child is a girl let B be: even number of girls let C be: 2 girls show that A and B are independent show that A and C are not independent 22.2 Inclusion/exclusion applied to probability Epp 6.8 recall | A B | = | A | + | B | - | A B | show that this implies, for equally likely outcomes, P ( A B ) = P ( A ) + P ( B )- P ( A B ) as it turns out, the result also applies to non-equally likely outcomes we will not prove this an example draw a card at random from an ordinary deck find probability of either a heart or an ace 22.3 Mutually exclusive events: P ( A B ) = 0 if P ( A B ) = 0 ( i.e. A B = ) then P ( A B ) = P ( A ) + P ( B ) A and B are mutually exclusive events contrast independent and mutually exclusive make sure that they are clear mutually exclusive are very dependent 22.4 Conditional probability Epp 6.9 general idea: if we have partial information about an experiment, it may modify our calculation of probability e.g. families of 2 children use Venn diagrams with S = { B 1 B 2 , B 1 G 2 , G 1 B 2 , G 1 G 2 } assuming outcomes are equally likely, show P (2 boys) = 1 4 show that, given that there is at least one boy, P (2 boys) = 1 3 use S = { B 1 G 2 , G 1 B 2 , B 1 B 2 } similarly, given that the first child is a boy, P (2 boys) = 1 2 use S = { B 1 G 2 , B 1 B 2 } definition: P ( A | B ) = P ( A B ) P ( B ) how do we read this?...
View Full Document

This note was uploaded on 04/19/2008 for the course ECE 190 taught by Professor Carter during the Fall '06 term at University of Toronto- Toronto.

Page1 / 6

f2006lecNotesWeek08 - 22 Probability (cont.) 22.1...

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

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