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

Step-by-step solution

Let A and B denote the events P speaks the truth and Q speaks the truth respectively. Given P ( A ) = 70 100 and P ( B ) = 80 100 Hence, P A ¯ = 1 - P ( A ) and P ( B ¯ ) = 1 - P B ⇒ P A ¯ = 1 - 70 100 = 30 100 and P B ¯ = 1 - 80 100 = 20 100 . We have to find the probability that they agree in stating the same fact this means either both of them are stating it correctly or both of them are stating it wrongly. The required probability is = P A P B + P A ¯ P B ¯ = 70 100 80 100 +