Counting - Le arning Obje s ctive fine pling with / without...

This preview shows pages 1–9. Sign up to view the full content.

Learning Objectives Define sampling with / without replacement and order / unordered and relate to counting methods Calculate probabilities using the counting principle by selecting the correct method or combination of methods: k-permutations combinations partitions

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

View Full Document
Example Polymers are to be created from three kinds subunits. There are 4 subunits of type A, 3 of type B, and 2 of type C. How many different 9-unit polymers are possible?
Counting Principle Consider a process that consists of r stages. Suppose that: There are n 1 possible results at the first stage For every possible result of the first stage, there are n 2 possible results at the second stage More generally, for any possible results of the first i-1 stages, there are n i possible results at the ith stage Then, the total number of possible results of the r-stage process is: n 1 n 2 …n r Example: roll 2 dice – 6*6=36 possible results

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

View Full Document
Exercises Exercise #1 Exercise #2
Questions to Ask Do we care about the order in which objects are selected? Ordered UnOrdered example: order of the cards you draw in poker doesn’t matter Do we get to reuse objects? With Replacement Without Replacement

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

View Full Document
Approaches Ordered UnOrdered With Replacement Without Permutations Combinations n ! ( n - k )! n * n * L = n k n k = n ! k !( n - k n + k - 1 k
Ordered Sampling With Replacement Care about the order objects are selected When an object is selected it can be re-selected Count possibilities using: select k from n n * n * L = n k

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

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

This note was uploaded on 02/22/2010 for the course BME 335 taught by Professor Dunn during the Spring '10 term at University of Texas at Austin.

Page1 / 30

Counting - Le arning Obje s ctive fine pling with / without...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online