Probability P(E) = Number of favourable outcomes / Total number of outcomes. P(E) lies between 0 and 1. P(E) + P(Ē) = 1. An impossible event has P = 0; a sure event has P = 1.

The sample space is the set of all possible outcomes of an experiment. Events are subsets of the sample space. E.g., tossing a coin: S = {H, T}; rolling a die: S = {1,2,3,4,5,6}. Complementary events together cover the entire sample space.

Card experiments: a deck has 52 cards — 4 suits of 13 each. P(ace) = 4/52 = 1/13. Coin and dice experiments are standard. For two dice, the sample space has 36 outcomes. Always list outcomes systematically to avoid errors.

If P(E) is the probability of an event, then P(Ē) = 1 − P(E) where Ē is the complement. This is useful when direct calculation is tedious: P(at least one head in 3 tosses) = 1 − P(no heads) = 1 − 1/8 = 7/8. Standard experiments: (1) Single die: 6 outcomes; (2) Two dice: 36 outcomes; (3) Single card from 52-card deck: aces=4, kings=4, queens=4, hearts=13, face cards=12 (J+Q+K of all suits), red cards=26. Always list the sample space for small experiments.