A speaks the truth in 80% of cases, so A lies in 20% of cases.
B speaks the truth in 90% of cases, so B lies in 10% of cases.
P(A speaks truth) = 54
P(A lies) = 51
P(B speaks truth) = 109
P(B lies) = 101
A and B contradict each other when one speaks the truth and the other lies.
This happens in two cases:
- A speaks truth and B lies
- A lies and B speaks truth
For A speaks truth and B lies:
P(A speaks truth and B lies) = 54×101
=504
For A lies and B speaks truth:
P(A lies and B speaks truth) = 51×109
=509
Total probability of contradiction:
P(contradiction) = 504+509
=5013
Therefore, the probability that they contradict each other is 5013.