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contents Independence and Conditional Probability Independence Conditional Probability Independence and Conditional Probability Independence Events whose intersection is the empty set are independent events or mutually exclusive outcomes. For example, if a single die is rolled, it is an independent event because it cannot happen that both 1 and 2 are rolled together. On the other hand, the probability of 1 and an odd number can occur at the same time because 1 is already odd. Therefore, these events are not mutually exclusive results. Calculating the probabilities of independent events is relatively easy. In other words, the probabilities of an event of 1 or 2 in a single die trial are mutually independent and therefore the sum of their probabilities. $$P(1 \, \text{or} \, 2) =P(1)+P(2)= \frac{1}{6}+\frac{1}{6}=\frac{1}{3}$$ Contrary to the above, if events A and B are not independent events, the above sum is modified as...