Q.A die is loaded in such a way that the probability of the face with $j$ dots turning up is proportional to $j$ for $j = 1, 2, ..., 6$. What is the probability, in one roll of the die, that an odd number of dots will turn up?

For a random experiment whose outcomes are all equally likely (no outcome is preferred over any other), the classical definition assigns to an event $A$ the probability $P(A)=n(A)/n(S)$, the fraction of all outcomes that are favourable to $A$. This single ratio - favourable outcomes over total outcomes - is the computational engine of the whole chapter: once a sample space is built and the outcomes favouring an ev …