MAT 2379 Lecture Notes - Lecture 2: Almost Surely, Mutual Exclusivity, Blood Transfusion

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 2379
• Professor: Maryam Sohrabi

Document Summary

In this chapter, we study some simple techniques which allow us to calculate the probabilities of events. Figure 1: the shaded region represents the event a. P(s) = 1 and p(a) + p(a0) = 1. We denote by a0 the event that (cid:498)a fails(cid:499). Let a be the event (cid:498)they have only boys(cid:499). Then a0 is the event (cid:498)they have at least one girl(cid:499). Consider a random experiment with sample space s. we will assume that all the events below are subsets of s. Consider two events a and b which can not occur in the same time. These are called mutually exclusive (or disjoint) events. When we draw the venn diagrams, the regions inside the two curves representing a and b are not overlapping. P(a (cid:1515) b) = p(a or b) = p(a) + p(b) if a,b are mutually exclusive. P(a (cid:1514) b) = p(a and b) = p(cid:523) (cid:524) = (cid:882) if a,b are mutually exclusive.