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Mutually Exclusive Events
A set of events is said to be mutually exclusive if the occurrence of any one of the events precludes the occurrence of any of the other events for illustration, when tossing a coin, the events are a head or a tail these are said to be mutually exclusive because the occurrence of heads for instance implies that tails cannot and has not happened.
This can be represented in venn diagram as given below:
E1 ∩ E2 = Ø
E1 ∩ E2 ≠ Ø
Non-mutually exclusive events (independent events)
Consider a survey whether a random sample of registered voters is selected. For every voter selected their sex and political party affiliation are noted. The events "KANU" and "woman" are not equally exclusive since the selection of KANU does not preclude the possibly that the voter is also a woman.
Independent Events
Events are said to be independent when the occurrence of any type of the events does not affect the occurrence of the other(s).For illustration the outcome of tossing a coin is independent of the outcome of the preceding or succeeding toss.
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sin(2x+x)=sin2x.cosx+cos2x.sinx =2sinxcosx.cosx+(-2sin^2x)sinx =2sinxcos^2+sinx-2sin^3x =sinx(2cos^2x+1)-2sin^3x =sinx(2-2sin^2x+1)-2sin^3
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