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a speaks truth in 60% cases and b in 70% cases. in what % of cases are they likely to contradict each other in stating the same fact?

User Nick Otten
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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.

User Hardik Bhalani
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