Probability | Class 12 Mathematics Notes

Classical Definition of Probability

The classical definition of probability applies when the sample space is finite and all outcomes are equally likely to occur. According to this definition, the probability of an event E is given by the ratio of the number of favorable outcomes to the total number of outcomes in the sample space. Mathematically, P(E) = Number of favorable outcomes / Total number of outcomes. This definition assumes that each outcome has the same chance of occurring, which is true for well-designed random experiments like tossing a fair coin or rolling a fair die. The probability of an impossible event is 0, and the probability of a certain event (the entire sample space) is 1. The classical definition provides a simple way to calculate probabilities in many practical situations. However, it is limited to cases where outcomes are equally likely and the sample space is finite. Examples include calculating the probability of getting a head in a coin toss, or the probability of rolling a 4 on a die. This section also discusses properties of probability such as 0 ≤ P(E) ≤ 1, and the sum of probabilities of all simple events equals 1.

📊 Diagram: No specific diagrams, but often illustrated with equally spaced outcomes such as faces of a die or coin toss results.

🧪 Activity: Exercises involving calculation of probabilities using the classical definition for dice, coins, and card experiments.

🔗 Connection: Leads to the Axiomatic Approach to Probability, which generalizes the concept beyond equally likely outcomes.