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Compliment of EIf E is an event of sample space S and É is the event that E does not happen then P(É)=1P(E) É is called the compliment of E n(E) + n(É) = n(S) P(E) + P(É) = 1 Consider the example A room has 3 sockets for bulbs. From a collection of 8 bulbs out of which 4 are defective , 3 bulbs are selected at random and put in the sockets. Find the probability that the room is lit Solution As 3 bulbs are selected from 8 bulbs n(S) = ^{8}C_{3}== 56 ways Let A be the event that the room is lit This gives rise to 3 cases
This involves tedious calculations and lengthy work. Hence consider the event Á whih implies that the room is dark Á = ^{4}C_{3} == 4 ways P(Á) = 4/56 = 1/14 so P(A) = 1 P(Á)= 1 1/14 = 13/14 Solved Examples
