chap4 - 4 Probability Rules and Conditional Probability 4.1...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
4. Probability Rules and Conditional Probability 4.1 General Methods In the mathematical de fi nition of probability, an arbitrary event A is merely some subset of the sample space S . The following rules hold: 1. P ( S ) = 1 2. For any event A, 0 P ( A ) 1 It is also obvious from our de fi nitions in Chapter 2 that if A and B are two events with A B (that is, all of the simple events in A are also in B ), then P ( A ) P ( B ) . It is often helpful to use elementary ideas of set theory in dealing with probability; as we show in this chapter, this allows certain rules or propositions about probability to be proved. Before going on to speci fi c rules, we’ll review Venn diagrams for sets. In the drawings below, think of all points in S being contained in the rectangle, and those points where particular events occur being contained in circles. We begin by considering the union ( A B ) , intersection ( A B ) and complement ( ¯ A ) of sets (see Figure 4.3). At the URL , there is an interesting applet which allows you to vary the area of the intersection and construct Venn diagrams for a variety of purposes. Example: Suppose for students fi nishing 2A Math that 22% have a math average 80%, 24% have a STAT 230 mark 80%, 20% have an overall average 80%, 14% have both a math average and STAT 230 80%, 13% have both an overall average and STAT 230 80%, 10% have all 3 of these averages 80%, and 67% have none of these 3 averages 80%. Find the probability a randomly chosen math student fi nishing 2A has math and overall averages both 80% and STAT 230 < 80%. Solution: When using rules of probability it is generally helpful to begin by labeling the events of interest. 29
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon