P, speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree in stating the same fact? Do you think when they agree, means both are speaking truth?

P(P speaking truth)

P(P speaking lie)

P(Q speaking truth)

P(Q speaking lie)

Cases when they agree in stating same fact are when they both speak truth or when they both speak lie.

⇒ P (stating the same fact) = 0.7× 0.8 + 0.3× 0.2

⇒ P (stating the same fact) = 0.56+0.06=0.62

Percentage of cases where they agree in stating the same fact = 0.62× 100 = 62%

No, they agree in stating the same fact does not mean both are speaking truth, they can be speaking lie.