-->

Probability

Question
CBSEENMA12033764

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Solution
 Let E1 denote the event that six occurs and E2 denote the event that it is not a six.
therefore         straight P left parenthesis straight E subscript 1 right parenthesis space equals 1 over 6 comma space space straight P left parenthesis straight E subscript 2 right parenthesis space equals 5 over 6
Let A denote the event that the man reports that it is six.
   therefore space space straight P left parenthesis straight A divided by straight E subscript 1 right parenthesis space equals space Probability space that space the space man space speaks space truth space equals space 3 over 4
         straight P left parenthesis straight A divided by straight E subscript 2 right parenthesis space equals space Probability space that space the space man space tells space straight a space lie space equals space 1 fourth
therefore      by Baye's Law
                straight P left parenthesis straight E subscript 1 divided by straight A right parenthesis space equals space fraction numerator straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight A divided by straight E subscript 1 right parenthesis over denominator straight P left parenthesis straight E subscript 1 right parenthesis. space straight P left parenthesis straight A divided by 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 A divided by straight E subscript 2 right parenthesis end fraction
space space space space space space space space space space space space space space space space equals space fraction numerator begin display style 1 over 6 end style cross times begin display style 3 over 4 end style over denominator begin display style 1 over 6 end style cross times begin display style 3 over 4 end style plus begin display style 5 over 6 end style cross times begin display style 1 fourth end style end fraction space equals fraction numerator 3 over denominator 3 plus 5 end fraction equals space 3 over 8

Some More Questions From Probability Chapter