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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        A bag contains 16 coins of which two are counterfeit with heads on both sides. The rest are fair coins. One coin is selected at random from the bag and tossed. The probability of getting a head is

    A)  \[\frac{9}{16}\]                               

    B)  \[\frac{11}{16}\]

    C)  \[\frac{5}{9}\]                                  

    D)  None of these

    Correct Answer: A

    Solution :

                    Let A be the event of selecting a counterfeit coin and B be the event of getting head. Then \[P(A)=\frac{2}{16},\]    \[P(\overline{A})=\frac{14}{16}\] and   \[P\left( \frac{B}{A} \right)=1,\] \[P\left( \frac{B}{A} \right)=\frac{1}{2}\]  Now, required probability                 \[=P(A\cap B)\cup P(\overline{A}\cap B)\]                 \[=P(A\cap B)+P(\overline{A}\cap B)\]                 \[=P(A)+P\left( \frac{B}{A} \right)+P(\overline{A})P\left( \frac{B}{A} \right)\]                 \[=\frac{2}{16}.1+\frac{14}{16}.\frac{1}{2}=\frac{9}{16}\]


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