Probability Basics

Complement Rule

Use the complement event to compute probabilities via:

P(Eᶜ) = 1 - P(E)

This avoids recomputing the unfavourable outcomes directly.

complement-rule P(Eᶜ) = 1 - P(E)

Example

Find the probability of not E by subtracting from one.

highlighted = computed this step

Step 1 — Sample space

Count all equally likely outcomes.

total=6total= \hl{6}

Step 2 — Event probability

Compute the probability of event E.

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

Step 3 — Complement

Use one minus the event probability.

P(Ec)=1−12=12P(E^c)= 1 - \frac{1}{2} = \hlmath{\frac{1}{2}}

Step 4 — Result

State the complement probability.

P(Ec)=12P(E^c)= \hlmath{\frac{1}{2}}