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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 34

  • question_answer
    A football match may be either won, drawn or lost by the host country's team. So, there are three ways of forecasting the result of any one match, one correct and two incorrect. Then the probability of forecasting at least three correct results for four matches, is -

    A) \[\frac{1}{9}\]   

    B)        \[\frac{2}{9}\]    

    C) \[\frac{2}{7}\]              

    D)        None

    Correct Answer: A

    Solution :

    [a] p = P (correct forecasting) \[=\frac{1}{3}\] q = P (wrong forecasting) \[=\frac{2}{3}\] n=4 let r be the number of correct forecast P(At least three correct results). \[=P\left( r=3 \right)+P\left( r=4 \right)\] \[P{{=}^{4}}{{C}_{3}}{{\left( p \right)}^{3}}{{\left( q \right)}^{1}}{{+}^{4}}{{C}_{4}}{{\left( p \right)}^{4}}{{\left( q \right)}^{0}}\] \[P=4{{\left( \frac{1}{3} \right)}^{3}}\left( \frac{2}{3} \right)+{{\left( \frac{1}{3} \right)}^{4}}\] \[={{\left( \frac{1}{3} \right)}^{3}}\left( \frac{8}{3}+\frac{1}{3} \right)\] \[=3\times \frac{1}{27}=\frac{1}{9}\]   


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