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A speaks the truth in 70% cases and B in 80% cases. The probability that they will
contradict each other in describing a single event is
  • a)
    0.36
  • b)
    0.38
  • c)
    0.62
  • d)
    0.42
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
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.
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Community Answer
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)
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