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Often it is taken that a truthful person commands, more respect in the society. A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a six.
Find the probability that it is actually a six.
Do you also agree that the value of truthfulness leads to more respect in the society?


Let H1 be the event that 6 appears on throwing a die
H2 be the event that 6 does not appear on throwing a die
E be the event that he reports it is six
straight P left parenthesis straight H subscript 1 right parenthesis space equals space 1 over 6 comma space straight P left parenthesis straight H subscript 2 right parenthesis space equals space 1 minus 1 over 6 space equals space 5 over 6
straight P left parenthesis straight E divided by straight H subscript 1 right parenthesis space equals space 4 over 5 comma space straight P left parenthesis straight E divided by straight H subscript 2 right parenthesis space equals space 1 fifth
straight P left parenthesis straight H subscript 1 divided by straight E right parenthesis space equals space fraction numerator straight P left parenthesis straight H subscript 1 right parenthesis. straight P left parenthesis straight E divided by straight H subscript 1 right parenthesis over denominator straight P left parenthesis straight H subscript 1 right parenthesis. straight P left parenthesis straight E divided by straight H subscript 1 right parenthesis space plus straight P left parenthesis straight H subscript 2 right parenthesis straight P left parenthesis straight E divided by straight H subscript 2 right parenthesis end fraction
space equals space 4 over 9
Yes ruthless leads to more respect in the society.

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