Probability Basics

Simple Probability

Compute the probability of a simple event from the ratio:

P(E) = favorable outcomes / total outcomes

where the event space is equally likely.

Example

Compute probability as favorable outcomes over total outcomes. This favorable-over-total formula is only valid when every outcome is equally likely; the book assumes that condition rather than establishing it.

highlighted = computed this step

Step 1 — Sample space

Count all equally likely outcomes.

total=6total= \hl{6}
6 equally likely outcomes123456

Step 2 — Favorable outcomes

Count the favorable outcomes for event E.

favorable=3favorable= \hl{3}
3 favorable outcomes123456

Step 3 — Build the fraction

Put favorable outcomes over total outcomes.

P(E)=3/6P(E)= \hl{3} / \hl{6}
3 of 6 outcomes123456

Step 4 — Simplify

Simplify the favorable-over-total fraction.

P(E)=3/6=12P(E)= 3 / 6 = \hlmath{\frac{1}{2}}
3 of 6 outcomes123456

Step 5 — Result

State the simple probability.

P(E)=12P(E)= \hlmath{\frac{1}{2}}
3 of 6 outcomes123456
simple-probability P(E) = # favorable / # total