Probability Distribution

What is a Probability Distribution Anyway?

Imagine you're playing a game of rolling dice. A probability distribution is like a complete list of all possible outcomes when you roll the dice, plus it tells you how big the chance (probability) is for each outcome to appear. Simply put, it's a list of possibilities and how often they happen.

Getting to Know the Sample Space (All Possible Outcomes)

The sample space is like the collection of all outcomes that can happen in an experiment. We usually write it using the symbol $\Omega$ (Omega).

Outcome $x$	Probability $P(x)$
$1$	$1/6$
$2$	$1/6$
$3$	$1/6$
$4$	$1/6$
$5$	$1/6$
$6$	$1/6$

Sum of Numbers $j$	Possible Pairs	Number of Pairs	Probability $P(j)$
$2$	$(1,1)$	$1$	$1/36$
$3$	$(1,2), (2,1)$	$2$	$2/36$
$4$	$(1,3), (2,2), (3,1)$	$3$
$5$	$(1,4), (2,3), (3,2), (4,1)$
$6$	$(1,5), (2,4), (3,3), (4,2), (5,1)$
$7$	$(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)$
$8$	$(2,6), (3,5), (4,4), (5,3), (6,2)$
$9$	$(3,6), (4,5), (5,4), (6,3)$
$10$	$(4,6), (5,5), (6,4)$	$3$
$11$	$(5,6), (6,5)$	$2$	$2/36$
$12$	$(6,6)$	$1$	$1/36$

Probability Distribution

What is a Probability Distribution Anyway?

Getting to Know the Sample Space (All Possible Outcomes)

Probability Distribution

What is a Probability Distribution Anyway?

Getting to Know the Sample Space (All Possible Outcomes)

Events and Their Probabilities

What is an Event?

Calculating the Probability of an Event

Rules of the Game for Probability Distributions

Rolling One Die

Rolling Two Dice

Probability Distribution for the Sum of Two Dice

Why is Learning Probability Distribution Important?