College Math

College Math Study Guide

©2018 of 120 4.7 Complement of an Event Suppose there is a medical box in which there are 15 different medicines, out of which four have been expired. Now you draw two medicines; what is the probability that the medicines drawn are NOT expired? Here, we use the concept of complement of an event. Complement of an event denotes all those set of outcomes which are not a part of event E. When an event is denoted by E, the complement of an event is denoted by E’. The probability of the complement of an event would be the total probability (that is 1) less the probability of the event E. Mathematically: P (E’) = 1 - ( ) ( ) The complement of an event can be viewed using the following Venn diagram: In the above diagram, if A is an event, then A’ is the complement of the event A. In the above example, the probability of not drawing expired medicine would be 1 less the probability of drawing the expired medicine. It will be calculated as follows: n(S) = C(15, 2) = 105 n(E) = C(4, 2) = 6 P (E) = 6/105 = 0.0571 The probability of not drawing any expired medicine would be: 1 – P(E) = 1 – 0.0571 = 0.9429 Achieve Page 69