Question

1. The odds that a person A speaks the truth is 8:9 and the odds that person B speaks the truth is 5:7. In what percentage of cases are they likely to contradict each other on an identical point 

Answer 1

P(A speaks the truth)= $\frac{8}{8+9}= \frac{8}{17}$

P(A speaks a lie)= $\frac{9}{8+9}= \frac{9}{17}$

P(B speaks the truth)= $\frac{5}{5+7}= \frac{5}{12}$

P(B speaks a lie)=$\frac{7}{5+7}= \frac{7}{12}$

They will contradict each other when A tells the truth/ B tells a lie or A tells a lie /B tells the truth

P(contradict)=$\frac{8}{17}*\frac{7}{12} +\frac{9}{17}*\frac{5}{12}$

=$\frac{56}{204}+\frac{45}{204}$

=$\frac{101}{204}$

=0.495.

hence the percentage is 49.5%.