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An example of calculating the probability of intersections of events in probability theory using the given sample space s = {1, 2, 3, 4} and associated probabilities p({1}), p({2}), p({3}), and p({4}). The document also shows that the events e1 = {1, 3}, e2 = {2, 3}, and e3 = {3, 4} are not independent by demonstrating that their intersection's probability does not equal the product of their individual probabilities.
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Suppose S = { 1 , 2 , 3 , 4 } and
Show that: P (E 1 ∩ E 2 ∩ E 3 ) = P (E 1 )P (E 2 )P (E 3 ) but that no pair of events E 1 ,E 2 , and E 3 are independent and hence E 1 ,E 2 , and E 3 are not independent.
