In other words, the additional information really
amounts to telling us that the situation may be considered as being that of a new
random experiment for which the sample space consists of all those outcomes only
which are favourable to the occurrence of the event F Now, the sample point of F which is favourable to event E is THH Thus, Probability of E considering F as the sample space = 1
4 ,
or
Probability of E given that the event F has occurred = 1
4
This probability of the event E is called the conditional probability of E given
that F has already occurred, and is denoted by P (E|F) Thus
P(E|F) = 1
4
Note that the elements of F which favour the event E are the common elements of
E and F, i