Question 698174
probability that the man you ask is the one who tells the truth 2 times out of 3 = {{{1/2}}}
{{{2/3}}} = probability of getting a true answer if you ask that guy.
probability that the man you ask is the other man = {{{1/2}}}
{{{x}}} = fraction of the times the other man tells the truth
(in other words the probability that his answer would be true).
 
If you ask one of the two men a question, your probability of getting a true answer is
{{{(1/2)*(2/3)+(1/2)*x=17/24}}}
{{{1/3+(1/2)*x=17/24}}}
{{{(1/2)*x=17/24-1/3}}}
{{{(1/2)*x=17/24-8/24}}}
{{{(1/2)*x=9/24}}}
{{{2*(1/2)*x=2*(9/24)}}} --> {{{x=9/12)}}} --> {{{highlight(x=3/4)}}}