Probability

probability-theory

Definition

Probability

Probability is a measure of uncertainty of the occurrence of an event, with an event being all desired outcomes out of all possible outcomes.

Examples

Fair Coin Toss

What is the probability of getting exactly 1 head out of 3 tosses?

Sample Space: Listing all $8$ possible outcomes:

$$\Omega =\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}$$

Event (Probability Theory): There are 3 outcomes in the “exactly 1 head”event

$$A=\{HTT,THT,TTH\}\subseteq \Omega$$

Probability: With all outcomes being equally likely, we get:

$$P(A)=\frac{|A|}{|\Omega |}=\frac{3\text{outcomes with}1\text{head}}{8\text{possible outcomes}}=\frac{3}{8}\approx 37.5\%$$