A speaks the truth in 70% cases and B in 80% cases. The probability t...
Explanation:
Given:
- A speaks the truth in 70% cases (i.e., probability of A speaking truth, P(A) = 0.7)
- B speaks the truth in 80% cases (i.e., probability of B speaking truth, P(B) = 0.8)
Finding the probability that they will contradict each other:
To find the probability that A and B will contradict each other in describing a single event, we need to consider the cases where one of them speaks the truth and the other lies.
Case 1: A speaks the truth and B lies:
- Probability of A speaking the truth: 0.7
- Probability of B lying (speaking falsehood): 1 - 0.8 = 0.2
- Probability of this case: 0.7 * 0.2 = 0.14
Case 2: A lies and B speaks the truth:
- Probability of A lying: 1 - 0.7 = 0.3
- Probability of B speaking the truth: 0.8
- Probability of this case: 0.3 * 0.8 = 0.24
Total probability of contradiction:
- Total probability = Probability of Case 1 + Probability of Case 2
- Total probability = 0.14 + 0.24 = 0.38
Therefore, the probability that A and B will contradict each other in describing a single event is 0.38, which corresponds to option B.
A speaks the truth in 70% cases and B in 80% cases. The probability t...
Probability that A and B will contradict each other is that A speaks truth and B lies
and B speaks truth. Let the probability be P(x). Probability of A speaking truth is P(A) and probability of B speaking truth isP(B)