STAT 2 Lecture Notes - Lecture 17: Venn Diagram, Normal Distribution, Null Hypothesis
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Ex: 2 events; chance of event a or probability of event a is . The probability of even b is 1/10; true or false: If a and b are independent, then they are mutually exclusive. P(b) - p(a and b) addition rule. P(a and b) = 0, so p(a or b) = p(a) + p(b) If we ignore the mutually exclusive part, p(a and b) = p(a) x p(b/a) = p(a) x. False, the events are not mutually exclusive because p(a and b) is not zero. If a and b are mutually exclusive, they cannot be independent. P(a) = , p(b) = 1/10, mutually exclusive, no overlap in venn diagram. A and b are independent if p(b/a) = p(b), p(b) = 1/10, p(b/a) = 0, because a and b are mutually exclusive; p(b/a) =/= p(b); that means a and b are not independent and the statement is true.
