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A speaks the truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?
- a)35
- b)30
- c)25
- d)20
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A speaks the truth in 75% and B in 80% cases. In what percentage of ca...
= 35%Most Upvoted Answer
A speaks the truth in 75% and B in 80% cases. In what percentage of ca...
A speak truth 75% i.e. P(A)=3/4, P(Ā)=1/4
similarly B speak truth 80% i.e. P(B)=4/5, P(B-)=1/5
while contradicting narration
probability = P(A)P(B-)+P(Ā)P(B)
= 3/4×1/5+1/4×4/5
= 7/20
=7/20×100%
=35%
option a is correct.....
similarly B speak truth 80% i.e. P(B)=4/5, P(B-)=1/5
while contradicting narration
probability = P(A)P(B-)+P(Ā)P(B)
= 3/4×1/5+1/4×4/5
= 7/20
=7/20×100%
=35%
option a is correct.....
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A speaks the truth in 75% and B in 80% cases. In what percentage of ca...
Calculation:
To calculate the percentage of cases in which A and B are likely to contradict each other, we need to find the probability of them narrating the same incident differently.
Probability of A speaking the truth:
- A speaks the truth in 75% of cases, so the probability of A speaking the truth is 0.75.
Probability of A not speaking the truth:
- The probability of A not speaking the truth is 1 - 0.75 = 0.25.
Probability of B speaking the truth:
- B speaks the truth in 80% of cases, so the probability of B speaking the truth is 0.80.
Probability of B not speaking the truth:
- The probability of B not speaking the truth is 1 - 0.80 = 0.20.
Probability of contradiction:
- The probability of A speaking the truth and B not speaking the truth is 0.75 * 0.20 = 0.15.
- The probability of A not speaking the truth and B speaking the truth is 0.25 * 0.80 = 0.20.
Total probability of contradiction:
- Total probability of contradiction = 0.15 + 0.20 = 0.35 = 35%.
Therefore, in 35% of cases, A and B are likely to contradict each other when narrating the same incident.
Therefore, the correct answer is option A) 35.
To calculate the percentage of cases in which A and B are likely to contradict each other, we need to find the probability of them narrating the same incident differently.
Probability of A speaking the truth:
- A speaks the truth in 75% of cases, so the probability of A speaking the truth is 0.75.
Probability of A not speaking the truth:
- The probability of A not speaking the truth is 1 - 0.75 = 0.25.
Probability of B speaking the truth:
- B speaks the truth in 80% of cases, so the probability of B speaking the truth is 0.80.
Probability of B not speaking the truth:
- The probability of B not speaking the truth is 1 - 0.80 = 0.20.
Probability of contradiction:
- The probability of A speaking the truth and B not speaking the truth is 0.75 * 0.20 = 0.15.
- The probability of A not speaking the truth and B speaking the truth is 0.25 * 0.80 = 0.20.
Total probability of contradiction:
- Total probability of contradiction = 0.15 + 0.20 = 0.35 = 35%.
Therefore, in 35% of cases, A and B are likely to contradict each other when narrating the same incident.
Therefore, the correct answer is option A) 35.
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A speaks the truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?a)35b)30c)25d)20e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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