Amazing Conditions

Abstract

The results obtained in the last chapter, using the basic rules for operating with probabilities, were in perfect agreement with common sense. From the present chapter onwards, many surprising results will emerge, starting with the inclusion of such a humble ingredient as the assignment of conditions to events. Consider once again throwing a die and the events ‘face less than or equal to 4’ and ‘even face’. In the last chapter we computed P(face less than or equal to 4) = 2/3 and P(even face) = 1/2. One might ask: what is the probability that an even face turns up if we know that a face less than or equal to 4 has turned up? Previously, when referring to the even-face event, there was no prior condition, or information conditioning that event.