probability theory

6. Independent Events: Two events are said to be independent if the occurrence of one event does not depend upon the other. This rule is known as the Theorem of Addition for Mutually Exclusive Events. When the events are overlapping, the theorem of addition determines the probability that one or more events would occur in a single trial. This is a case of overlapping events as some students who passed in Math may have passed in English too and some students who passed in English may have passed in Math too. Thus we need to remove these common students from the sum of students who passed in Math and English. Thus, using the theorem of addition for overlapping events, we get: When we have to determine the probability of joint occurrence or occurrence in unison of two or more than two events, the theorem of multiplication is used. For instance, the probability of getting the same number on two dice tossed simultaneously, drawing different coloured balls from a box having red, blue, and green balls. If this relationship does not hold true, events E1 and E2 are statistically not independent . Therefore, the overall chances that the policy will be introduced are 42%.