A and B speak the truth with probabilities 3/5 and 4/7 respectively. What is the likelihood they corroborate the same fact?
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Answer: A. 18/35
Explanation
Two people corroborate a fact if both speak the truth or if both choose to lie simultaneously. The probability that both individuals speak the truth is calculated as three-fifths multiplied by four-sevenths, equaling twelve thirty-fifths. The probability that both lie is two-fifths multiplied by three-sevenths, equaling six thirty-fifths, which sums to eighteen thirty-fifths. Probability theory calculates the likelihood that specific independent or dependent compound events will occur successfully. Mutually exclusive event probabilities are added together to find the total combined likelihood of multiple valid outcomes. Complementary probabilities represent the opposite chance of an event failing to happen, such as a person lying.
Option B accounts only for the scenario where both individuals speak the truth, ignoring joint lying outcomes. Option C represents an incorrect summation of the individual probability fractions calculated from the scenario. Option D miscalculates the cross-multiplication products of the truth and falsehood fractions for the two speakers.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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