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Probability

Question
CBSEENMA12033781
Wired Faculty App

Probability that A speaks truth is 4 over 5. A coin is tossed. A reports that a head appears. The probability that actually there was head is 
  • 4 over 5
  • 1 half
  • 1 fifth
  • 2 over 5

Solution

A.

4 over 5

Let E1, E2, E be the events
E1 : ‘coin comes up with a head’,
E2 : ‘coin comes up with a tail’,
E : ‘A reports that a head appears’
                  straight P left parenthesis straight E subscript 1 right parenthesis space equals space straight P left parenthesis straight E subscript 2 right parenthesis space equals space 1 half.
                 straight P left parenthesis straight E vertical line straight E subscript 1 right parenthesis space equals space straight P left parenthesis head space comes space up space and space straight A space speaks space truth right parenthesis space equals space 4 over 5
and           straight P left parenthesis straight E vertical line straight E subscript 2 right parenthesis space equals space straight P left parenthesis tail space comes space up space and space straight A space tells space straight a space lie right parenthesis space equals space 1 fifth
space therefore space space Required space probability space space equals space straight P left parenthesis straight E subscript 1 space vertical line thin space straight E right parenthesis
                                               equals space fraction numerator straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight E thin space vertical line thin space straight E subscript 1 right parenthesis over denominator straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight E vertical line straight E subscript 1 right parenthesis space plus space straight P left parenthesis straight E subscript 2 right parenthesis space straight P left parenthesis straight E vertical line straight E subscript 2 right parenthesis end fraction space equals space fraction numerator begin display style 1 half end style cross times begin display style 4 over 5 end style over denominator begin display style 1 half end style cross times begin display style 4 over 5 end style plus begin display style 1 half end style cross times begin display style 1 fifth end style end fraction equals space fraction numerator 4 over denominator 4 plus 1 end fraction space equals 4 over 5.
∴ (A) is correct answer.

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