Probability Outcomes and Models

A trial produces an outcome. The sample space is the set of all possible outcomes, and an event is a subset of that sample space. For equally likely outcomes, P(A)= number of outcomes in Atotal number of outcomes. Check equal likelihood before counting. Probabilities satisfy 0 <= P(A) 1, P(S)=1, and P(A)=1-P(A). An impossible event has probability zero; a certain event has probability one. Experimental relative frequency is number of occurrencesnumber of trials. It estimates a probability and can vary between samples. For a fair die, the theoretical probability of an even score is 3/6=1/2; observing 47 even scores in 100 throws gives relative frequency 0.47. A geometric area ratio represents probability only when the point is chosen uniformly over the region. For a point uniformly chosen in a square of area 20, an event region of area 5 has probability 5/20=1/4. A selection mechanism favouring one part of the square changes this calculation.