Probability

5 minQuiz at the end

What is Probability?

Probability measures how likely an event is to happen. It ranges from 0 (impossible) to 1 (certain).

P(event) = Number of favourable outcomes Γ· Total number of outcomes

The Probability Scale

0 ────────── 0.5 ────────── 1
impossible   even chance   certain

Calculating Probability

A bag has 3 red, 5 blue, and 2 green balls (10 total):

  • P(blue) = 5/10 = 1/2
  • P(not red) = 7/10

Complementary Events

P(event) + P(not event) = 1

If P(rain tomorrow) = 0.3, then P(no rain) = 1 - 0.3 = 0.7

Experimental vs Theoretical Probability

  • Theoretical: calculated from equally likely outcomes
  • Experimental: based on actual results of repeated trials

As the number of trials increases, experimental probability approaches theoretical.

Mutually Exclusive Events

Two events are mutually exclusive if they cannot both happen at the same time.

P(A or B) = P(A) + P(B) β€” for mutually exclusive events only.

Tree Diagrams

Tree diagrams show all possible outcomes of combined events, making it easy to calculate probabilities by multiplying along branches.