Probability — Class 12 Mathematics

This chapter develops probability beyond simple counting. Conditional probability measures the chance of given that has occurred. The multiplication theorem follows: . Two events are independent when . The Theorem of Total Probability sums the contributions of mutually exclusive, exhaustive events, and Bayes' Theorem reverses conditioning to find from the prior probabilities and likelihoods. A random variable assigns a number to each outcome; its probability distribution leads to the mean (expectation) and variance. The binomial distribution, modelling independent Bernoulli trials with success probability , gives .