Math 132A

Probability Distributions

Two dice example

Suppose we roll two dice and add the two numbers that show on the top of the dice.

Alternative Sample Space

Sum	2	3	4	5	6	7	8	9	10	11	12
Probability

Not equally likely outcomes!

Graphical Representation

2	3	4	5	6	7	8	9	10	11	12
\(1/32\)	\(2/36\)	\(3/36\)	\(4/36\)	\(5/36\)	\(6/36\)	\(5/36\)	\(4/36\)	\(3/36\)	\(2/36\)	\(1/36\)

A Biassed Coin

Outcome	Head	Tail
Probability	0.6	0.4

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Outcome	Head	Tail
Probability	\(p\)	\(q\)

\[p + q = 1\]

A Loaded Die

Outcome	1	2	3	4	5	6
Probability	.1	.15	.15	.15	.15

Colors of Snails

Certain species of snails can have 5 different color variations: yellow, brown, green, black, and blue. At certain location, 30% of the snails are yellow, 20% are brown, 5% are green, and 22% are black. We randomly select one of the snails and record its color.