A speaks truth in 75% cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?

To solve this problem, we need to consider two scenarios where A and B contradict each other.

1. Scenario 1: A tells the truth and B lies.
2. Scenario 2: A lies and B tells the truth.

Let's calculate the probability for each scenario:

1. Scenario 1: The probability that A tells the truth is 75% or 0.75. The probability that B lies is the complement of the probability that B tells the truth, which is 1 - 0.80 = 0.20 or 20%. So, the probability of both events happening is 0.75 * 0.20 = 0.15 or 15%.

2. Scenario 2: The probability that A lies is the complement of the probability that A tells the truth, which is 1 - 0.75 = 0.25 or 25%. The probability that B tells the truth is 80% or 0.80. So, the probability of both events happening is 0.25 * 0.80 = 0.20 or 20%.

Finally, to find the total probability that A and B contradict each other, we add the probabilities of these two scenarios: 0.15 + 0.20 = 0.35 or 35%.

So, A and B are likely to contradict each other in 35% of cases.