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A and B are two independent witnesses (i...

`A and B` are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is x and the probability that B will speak the truth is y. A and B agree in a certain statement. Show that the probability that the statement is true is `(xy)/(1-x-y+2xy)`.

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ARIHANT MATHS-PROBABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. A and B are two independent witnesses (i.e., there is no collision bet...

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  2. A person goes to office either by car, scooter, bus or train probabili...

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  3. A six faced fair die is thrown until 1 comes. Then , the probability t...

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  4. Let A and B be two events such that Poverline((AcupB))=(1)/(6),P(AcapB...

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  5. Three houses are available in a locality. Three persons apply for the ...

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  6. A randam variable X has Poisson's distribution with mean 2. Then , P(X...

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  7. There are n urns each containing (n+1) balls such that ith urn contain...

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  8. In a telephone enquiry system, the number of phone calls regarding rel...

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  9. One Indian and four American men and their wives are to be seated rand...

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  10. Let H1, H2,..., Hn be mutually exclusive events with P (Hi) > 0, i = ...

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  11. Let E^c denote the complement of an event E. Let E,F,G be pairwise ind...

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  12. A pair of fair dice is thrown independently three times. The probab...

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  13. Two aeroplanes I and II bomb a target in succession. The probabilit...

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  14. An experiment has 10 equally likely outcomes. Let A and B be two non-e...

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  15. Consider the system of equations ax + by = 0; cx + dy = 0, where a, b,...

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  16. A die is thrown. Let A be the event that the number obtained is gre...

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  17. It is given that the events A and B are such that P(A)=(1)/(4),P((A)/(...

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  18. A fair die is tossed repeatedly until a six is obtained Let X denote t...

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  19. A fair die is tossed repeated until a six is obtained. Let X denote th...

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  20. A fair die is tossed repeatedly until a six obtained. Let X denote the...

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  21. In a binomial distribution B(n , p=1/4) , if the probability of at lea...

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