An anti-aircraft gun can take a minimum of four shots at an enem
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    Probability

    Multiple Choice QuestionsLong Answer Type

    871.

    The probability of A solving a problem is 3 over 7 and that of B solving it is 1 third. What is the probability that
    (i)    at least one of them will solve the problem?
    (ii)    Only one of them will solve the problem?

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    Answer

    Multiple Choice QuestionsShort Answer Type

    872. A speaks truth in 60% cases and B in 90% cases. In what percentage of cases are they likely to contradict each other in stating the same fact.
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    Answer
    873. A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?
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    874. The probability of hitting a target by three marksmen are 1 half comma space 1 third space and space 1 fourth respectively. Find the probability that one and only one of them will hit the target when they fire simultaneously.
    83 Views
    Answer
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    875. An anti-aircraft gun can take a minimum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

    Let E1 , E2 , E3 , E4 be the events of hitting the plane by 1st, 2nd, 3rd, 4th shot respectively. Then
     straight P left parenthesis straight E subscript 1 right parenthesis space equals space 0.4 comma space space space straight P left parenthesis straight E subscript 2 right parenthesis equals space 0.3 comma space space space straight P left parenthesis straight E subscript 3 right parenthesis space equals space 0.2 comma space space space straight P left parenthesis straight E subscript 4 right parenthesis space equals space 0.1
    therefore space space space space straight P left parenthesis straight E with bar on top subscript 1 right parenthesis space equals space 0.6 comma space space straight P left parenthesis straight E with bar on top subscript 2 right parenthesis space equals space 0.7 comma space space straight P left parenthesis straight E with bar on top subscript 3 right parenthesis space equals space 0.8 comma space space straight P left parenthesis straight E with bar on top subscript 4 right parenthesis space equals space 0.9
    Probabililty that no shot hit the plane
                              equals space straight P left parenthesis straight E with bar on top subscript 1 space space straight E with bar on top subscript 2 space straight E with bar on top subscript 3 space stack straight E subscript 4 with bar on top right parenthesis equals space straight P left parenthesis straight E with bar on top subscript 1 right parenthesis thin space straight P left parenthesis straight E with bar on top subscript 2 right parenthesis space space straight P left parenthesis straight E with bar on top subscript 3 right parenthesis thin space straight P left parenthesis straight E with bar on top subscript 4 right parenthesis space equals space.6 space cross times space.7 space cross times space.8 space cross times space.9 space equals space.3024
    therefore   probability that at least one shot hit the plane.
                                equals space 1 minus straight P left parenthesis straight E with bar on top subscript 1 space space straight E with bar on top subscript 2 space straight E with bar on top subscript 3 space straight E with bar on top subscript 4 right parenthesis equals space 1 minus.3024 space equals space.6976
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    876. A problem is given to three students, whose chances of solving it are 1 third comma space 1 fifth space and space 1 over 6 respectively. What is the probability that exactly one of them may solve it?
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    877. A problem is given to three students, whose chances of solving it are 1 fourth comma space 1 third space and space 1 half respectively. Find the probability that exactly one of them may solve it.
    74 Views
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    878. The probabilities of A, B, C solving a problem are  1 third comma space 2 over 7 space and space 3 over 8 respectively. If all the three try to solve the problem simultaneously find the probability that exactly one of them will solve it.
    75 Views
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    879. A problem in Mathematics is given to three students Dayanand, Ramesh and Naresh and whose cances of solving it are 1 half comma space 1 third comma space 1 fourth respectively, what is the probability  that the problem will be solved?
    91 Views
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    Multiple Choice QuestionsLong Answer Type

    880. The probability of A hitting a target is 4 over 5 and that of B hitting it is 2 over 3. They both fire at the target. Find the probability that 
    (i) at least one of them will hit the target.
    (ii) only one of them will hit the target.
    73 Views
    Answer
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