Final answer:
Person A speaks the truth 60% of the time and person B speaks the truth 70% of the time; they will contradict each other if one tells the truth and the other lies. The combined probability of them contradicting each other is 46%.
Step-by-step explanation:
To find out the percentage in which person A and B are likely to contradict each other when stating the same fact, we need to look at the probabilities that they will tell the truth or lie.
A speaks the truth 60% of the time, which means A lies 40% of the time. Similarly, B speaks the truth 70% of the time, meaning B lies 30% of the time. They will contradict each other if one tells the truth and the other lies. This can happen in two ways: A tells the truth and B lies, or A lies and B tells the truth.
The probabilities of these two scenarios are:
- A tells the truth and B lies: 60% * 30% = 18%
- A lies and B tells the truth: 40% * 70% = 28%
We add these probabilities to find the overall percentage that they will contradict each other:
18% + 28% = 46%
Therefore, A and B are likely to contradict each other in 46% of the cases when stating the same fact.