A speaks truth in 80% cases and B speaks truth in 90% cases. In what percentage of cases are they likely to agree with each other in stating the same

Monjur Alahi

A speaks truth in 80% cases and B speaks truth in 90% cases. In what percentage of cases are they likely to agree with each other in stating the same fact ?


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Salim Ahmed Kawsar

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`P(A) =(80)/(100)=(4)/(5), P(B)=(90)/(100)=(9)/(10)`
P(Agree)=P(Both speaking truth or both telling lie)
`=P(AB or barAbar B)`
` P(A)P(B)or P(barA)P(barB)`
`=(4)/(5)(9)/(10)+(1)/(5)(1)/(10)`
`=(36+1)/(50)=(37)/(50)`
`=(74)/(100)=74%`

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