The odds that 2 personsA and B speak truth are 7:2 and 3:4 respectively.in what percentage of case are they likely to contradict on the identical fact?persons A and B speak truth 7:2 and3:4 respectively
In what percentage of case are they likely to constradict on an identical fact
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There are 4 potential outcomes, with their respective probabilities:
A and B tell truth: 3/(3+2) * 7/(7+3) = 3/5 * 7/10 = 21/50, or 42%
A and B lie: 2/5 * 3/10 = 6/50, or 12%
A tells truth and B lies: 3/5 * 3/10 = 9/50, or 18%
A lies and B tells truth: 2/5 * 7/10 = 14/50, or 28%
They agree whether they both tell the truth or both lie, so we can conclude:
Probability of agreement = 42% + 12% = 54%
Probability of contradiction = 18% + 28% = 46%
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