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Probability

Question
CBSEENMA12033664

A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : “the number of heads is odd”.   
F : “the number of tails is odd”.

Solution

Here,   S = {HHH,  HHT,  HTH,  THH, TTH, THT,  HTT, TTT}
        P(E) = P(HHH,   TTH, THT, TTH) = 4 over 8 space equals 1 half
        straight P left parenthesis straight F right parenthesis space equals space straight P left parenthesis HHT comma space HTH comma space THH comma space TTT right parenthesis space equals 4 over 8 space equals space 1 half
         straight P left parenthesis straight E intersection straight F right parenthesis space equals space 0
therefore space space space space straight P left parenthesis straight E intersection straight F right parenthesis space not equal to space straight P left parenthesis straight E right parenthesis space cross times space straight P left parenthesis straight F right parenthesis space space space space space space space space space space space space space space space space space space open square brackets because space space 0 space not equal to space 1 half cross times 1 half close square brackets
therefore space space space events space straight E space and space straight F space are space not space independent.
   
     

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