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What is the probability that the two contradict each other if, of two witnesses, A is...

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xetaalpha | Student | Honors

Posted September 3, 2012 at 2:30 PM via web

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What is the probability that the two contradict each other if, of two witnesses, A is 75% likely to say the truth and B is 35% likely to say the truth?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 3, 2012 at 2:35 PM (Answer #1)

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Of the two witnesses A is 75% likely to say the truth and B is 35% likely to say the truth. The two will not contradict each other if either both lie or both say the truth.

The probability of A lying is 25% and the probability of B lying is 65%. The probability that the two contradict each other is equal to the sum of the probability of either of them lying and the other saying the truth. This is equal to 0.75*0.65 + 0.35*0.25 = 0.575 = 57.5%

There is a 57.5% probability that the two contradict each other.

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