# CS6015: Linear Algebra and Random Processes

## Lecture 23:  Counting Principles : Very Simple Counting, Multiplication Principle

### Machine Learning

P(label = cat | image) ?

0.7

0.2

0.1

### What is the probability of getting a heads?

\frac{1}{2}~or~50\%

### What is the probability of getting a 6?

\frac{1}{6}~or~16.67\%

\frac{1}{n}

n ?
\cdots

n ?

\cdots

\cdots

\div 7

+ 1
\div 4

### How many numbers are there in this sequence ?

+ 2
* 12
9\frac{5}{12}, 9\frac{5}{6}, 10\frac{1}{4}, \dots, 21\frac{1}{2}, 21\frac{11}{12}, 22\frac{1}{3}
\frac{113}{12}, \frac{118}{12}, \frac{123}{12}, \dots, \frac{258}{12}, \frac{263}{12}, \frac{268}{12}
113, 118, 123, \dots, 258, 263, 268
115, 120, 125, \dots, 260, 265, 270
\div 5
23, 24, 25, \dots, 52, 53, 54