11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-1

  • question_answer 3) A boy contains 10 apples and of which 4 be rotten. Two apples are taken out together. If one of them is found to be good, the probability that other is also good is

    A) \[\frac{8}{15}\]                         

    B) \[\frac{5}{18}\]  

    C) \[\frac{2}{3}\]                          

    D) \[\frac{1}{3}\]

    Correct Answer: B

    Solution :

    [b] Total no. of ways of selecting 2 good apples   \[{{=}^{6}}{{C}_{2}}=\frac{\left| \!{\nderline {\,   6 \,}} \right. }{\left| \!{\nderline {\,   2 \,}} \right. .\left| \!{\nderline {\,   4 \,}} \right. }=\frac{6\times 5}{2}\] \[=15\And \]total no. of ways so that at least one of the two selected apples is good \[{{=}^{6}}{{C}_{1}}{{\times }^{9}}{{C}_{1}}=6\times 9\] = 54 Hence the required probability \[=\frac{15}{54}=\frac{5}{18}\]Hence, option is correct.          

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