Probability

Formula / Rule

Probability

Topic

Statistics

Formula

P(E) = Favourable outcomes / Total outcomes

P(E) range: $0 \le P(E) \le 1$

Complement: $P(E') = 1 - P(E)$

Addition rule: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

For mutually exclusive events: $P(A \cup B) = P(A) + P(B)$

Multiplication rule (independent events): $P(A \cap B) = P(A) \times P(B)$

When to Use

Dice, cards, coin, or any random experiment problems.

Worked Example

Q: A die is rolled. What is $P(\text{even number})$?

Favourable = ${2, 4, 6} = 3$ Total = 6 $P = 3/6 = \textbf{1/2}$