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Probability

Question
CBSEENMA12033663
Wired Faculty App

A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : “the number of heads is two”.
F : “the last throw results in head”.

Solution

Here,   S = {HHH,  HHT,  HTH,  THH, TTH, THT,  HTT, TTT}
   straight P left parenthesis straight E right parenthesis space equals space straight P left parenthesis HHT comma space space HTH comma space THH right parenthesis space equals space 3 over 8 straight P left parenthesis straight F right parenthesis space equals space left parenthesis HHH comma space HTH comma space THH comma space TTH right parenthesis space equals space 4 over 8 space equals space 1 half straight P left parenthesis straight E space intersection space straight F right parenthesis space equals space straight P left parenthesis HTH comma space space THH right parenthesis space equals space 2 over 8 space equals space 1 fourth therefore space space space space straight P left parenthesis straight E space intersection space 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 space space space space space space open square brackets because space 1 fourth not equal to 3 over 8 cross times 1 half close square brackets therefore space events space straight E space and space straight F space are space not space independent. space
     

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