Motivating example

Roll a die, what is the probability of getting a number < 4 and even?

• Set of possible results is {1,2,3,4,5,6} is the sample space

• Two events of interest, as sets:

  $E_1 = \{1,2,3\}$ (‘less than 4’)

  $E_2 = \{2,4,6\}$ (‘even’)

• Combined, even and less than 4 is the intersection of E1 and E2:

  $E = E_1 \cap E_2 = \{2\}$

• The probability is the measure of E relative to the the sample space, here $1/6$ since the measure here is just a counter.

• Mathematical approach is independant of interpretation (Frequentist, Bayesian, others?)