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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-1

  • question_answer
    If the chance that a ship will arrive safely at a port, is \[\frac{9}{10}\], the chance that out of 5 ships expected to arrive at the port, at least 4 will arrive safely, is

    A)  \[\frac{91854}{100000}\]                      

    B)  \[\frac{91827}{100000}\]       

    C)  \[\frac{91881}{100000}\]          

    D)  None of these

    Correct Answer: A

    Solution :

    [a] Here \[n=5,p=P\] (safe arrival of 1 ship) \[=\frac{9}{10},q=\frac{1}{10}\] Hence \[P(4)+R(5){{=}^{5}}{{C}_{4}}{{(9/10)}^{4}}{{(1/10)}^{1}}{{+}^{5}}{{C}_{5}}{{(9/10)}^{5}}{{(9/10)}^{0}}\]\[=\frac{32805+59049}{{{10}^{5}}}=\frac{91854}{100000}\]


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