Introduction
Probability measures how likely an event is to occur, using the same counting techniques from Permutation &
Combination to count favourable and total outcomes.
Core Formula
Probability of an event = (Number of favourable outcomes) / (Total number of possible outcomes)
Probability always lies between 0 and 1. P(not A) = 1 − P(A).
Q. A bag contains 5 red and 3 blue balls. If one ball is drawn at random, find the probability that it is blue.
Total balls = 5+3 = 8. Favourable (blue) = 3. Probability = 3/8.
Q. A bag contains 4 red and 6 green balls. Two balls are drawn at random. Find the probability that both are green.
Total ways to draw 2 from 10 = ¹⁰C₂ = 45. Favourable ways (both green from 6) = ⁶C₂ = 15.
Probability = 15/45 = 1/3.
Q. Two dice are thrown together. Find the probability that the sum of the numbers is 8.
Total outcomes = 6×6 = 36. Favourable pairs summing to 8: (2,6),(3,5),(4,4),(5,3),(6,2) = 5 outcomes.
Probability = 5/36.
⚠️ Key Insight: For "at least one" probability questions, it's usually faster to calculate
P(none) first and subtract from 1, rather than adding up every "at least" case separately.
✅ Practice Focus: Ball/bag-drawing probability using combinations · Dice and coin classical
probability · "At least one" problems using the complement rule.