Here are the course lecture notes for the course MAS108, Probability I, at Queen Mary, University of London, taken by most Mathematics students and some others in the first semester.

This chapter introduces students to the basics of probability. The emphasis is on problems that occur naturally, both in the playing of games and in natural phenomena.

It presents a thorough treatment of probability ideas and techniques necessary for a ̄rm understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.

The probability of the sample space is one. Independent events: The occurrence of any one of the events does not affect the probabilities of the occurrences of the other events.

What is probability? The probability of an event is its relative frequency (expected proport. on) in the long run. If an event occurs x times out of n, then its probability will converge on x ÷ n as n beco. es …

Using this model, the probability that the outcome lies in a given set E [0; 1] is equal to the Lebesgue measure of E. For example, the probability that the outcome is rational is 0, and the probability that …

Key Probability Definitions and Notation Probability is a number between 0 and 1 that is assigned to a possible outcome of a random circumstance. A simple event is a unique possible outcome of a …