Introduction

There are basic rules to which all probabilities must conform. Thus the manner in which probabilities of compound events are derived from those of simple events is quite invariant and independent of the methods by which the probabilities of the simple events have been initially obtained.

All probabilities are non-negative and expressed on a scale from 0 to 1. (Occasionally the scale is expressed in percentage terms from 0 to 100.) The greatest degree of probability which any future event can have is certainty, and the scale assigns this a probability of 1.00 (or 100%). At the other end of the scale, the lowest degree of probability that a future event can have is ‘impossibility’ to which is assigned a probability of zero. The next two sections introduce the basic rules for the addition and multiplication of probabilities when compound events are concerned.

Addition of probabilities

A stationery shop stocks three types of stapling machine. Examination of past records shows that 40% of customers purchase a machine of type A, 35% one of type B, and 25% of type C. Types A and B are made by manufacturer X, type C by manufacturer Y. A customer comes in to buy a stapling machine; what is the probability that he will buy one made by manufacturer X?

Denote by P(A) the probability that a machine of type A is purchased, etc. and by P(A + B) the probability that either type A or type B is purchased. Then Then

P(A) = 0.4, P(B) = 0.35 and P(A + B) = 0.75