204 5.2%2c5.3%2c5.4 Properties of Probability

# 204 5.2%2c5.3%2c5.4 Properties of Probability - valid for...

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

5.2 Properties of Probability Compliments and The Addition Rule From the above definitions we can quickly develop a few properties of probability . For example, the probability of an event (E) can be no less than 0(it never occurs) and no more than 1 ( it always occurs) 0 P(E) 1 Also (probability of E occurring)+(probability of E not occurring)= 1 P(E) + P( not E) = 1 Addition Rule Mutually Exclusive Events If a sequence events (E 1 , E 2, E 3 , . . . E n ) are mutually exclusive the probability of their union is: P(E 1 or E 2 or E 3 , … or E n ) = P(E 1 ) + P(E 2 ) + . .. + P(E n ) Example: Assume you randomly take a ball from a container that contains 3 red balls, 5 blue balls, 8 yellow balls, and 2 orange balls (total = 18 balls); what is the probability of a red or orange ball if one ball is randomly selected. P(red or orange) = 3/18 + 2/18 = 5/18 General “Addition” Rule for the union of events (i.e. it is

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: valid for mutually exclusive or non-exclusive events) P(A or B) = P(A) + P(B) - P(A and B) A C B 5.3 Multiplication Rule For Independent Events If E 1 , E 2, E 3 , . . . E n independent events, the probability of their intersection is: P(E 1 and E 2 and E 3 , … and E n ) = P(E 1 ) * P(E 2 ) * . .. * P(E n ) Example1: Roll a die and select a card from a deck of 52 cards. Specifically, find the probability of rolling a 4 and selecting a club = P(4)*p(club) = 1/6 * 1/4 = 1/24 Example 2 5.4 General “Multiplication” Rule and Conditional Probability for the intersection of events Note: P(A|B) = the probability of A given that B has occurred The probability of A given B is: P(A|B) = P(AB)/P(B) The probability of B given A is: P(B|A) = P(AB)/P(A) Thus the probability of A and B is: P(AB) = P(A|B)P(B) = P(B|A)P(A) B A A C B...
View Full Document

## This note was uploaded on 12/05/2011 for the course MATH 2040 taught by Professor Raysievers during the Fall '10 term at Utah Valley University.

### Page1 / 2

204 5.2%2c5.3%2c5.4 Properties of Probability - valid for...

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

View Full Document
Ask a homework question - tutors are online