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Probability

Question
CBSEENMA12033605

A coin is tossed three times, where
E : head on third toss,     F : heads on first two tosses

Solution

Here S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
E : head on third toss
 therefore    E = {HHH, HTH, THH, TTH}
and F : heads on first two tosses
therefore space space space straight F space equals space left curly bracket HHH comma space HHT right curly bracket
therefore space space straight E intersection straight F space equals space left curly bracket HHH right curly bracket
therefore space space straight P left parenthesis straight E right parenthesis space equals space 4 over 8 space equals space 1 half comma space space space straight P left parenthesis straight F right parenthesis space equals space 2 over 8 space equals space 1 fourth comma space space space straight P left parenthesis straight E intersection straight F right parenthesis space equals space 1 over 8
                 straight P left parenthesis straight E space left enclose straight F right parenthesis space equals space fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals fraction numerator begin display style 1 over 8 end style over denominator begin display style 2 over 8 end style end fraction space equals space 1 half 

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