Introduction to Probability

About the lecture

In this mini-lecture, we give an introduction to probability. We think about: (i) the definition of probability: the study of randomness and chance; (ii) applications of probability in machine learning, biology, statistics, and physics; (iii) a motivating example from genetics where we see how probability can be used to predict alleles of offspring; (iv) how probability is used to estimate or calculate the likelihood of an event occurring; (v) examples of calculating probability and their corresponding chances using a sliding scale: flipping a fair coin, rolling a fair six-sided die; (vi) the equation describing the probability of an outcome: probability of an outcome (event) = number of ways the outcome occurs / the number of possible outcomes; (vii) the notation used to describe the probability of an event: P[Event]; (viii) examples of calculating probabilities; and (ix) a non-examinable remark on probability from two philosophical perspectives: the approach made by ‘Frequentists’ and the approach made by ‘Subjectives/Bayesians.’

About the lecturer

Sunil Chhita is an Associate Professor of Probability in the Department of Mathematical Sciences at Durham University. His research interests include probability theory and statistical mechanics, in particular the dimer model, the six vertex model, and alternating sign matrices. He has studied the rough-smooth transition, a transition between exponential and polynomial decay of correlations, which appears naturally in the two-periodic Aztec diamond. More recently, he has been studying the so-called liquid-gas transition which naturally appears for domino tilings of the two-periodic Aztec diamond.