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10th Class Mathematics Probability Question Bank Probability

  • question_answer
    A jar contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is \[\frac{1}{3},\] and the probability of selecting a green marble at random is \[\frac{4}{9}.\].How many white marbles does the jar contain?

    A)  12                  

    B)  6                    

    C)  9                                

    D)  11                  

    Correct Answer: A

    Solution :

    Let there be b blue, g green and w white marbles in the jar. Then,\[b+g+w=54\] ?.(i) \[\therefore \]   P (Selecting a blue marble) \[=\frac{b}{54}\] It is given that the probability of selecting a blue marble is \[\frac{1}{3}\]. \[\therefore \]  \[\frac{1}{3}=\frac{b}{54}\Rightarrow b=18\]                     We have, P (Selecting a green marble) \[=\frac{4}{9}\] (given) \[\Rightarrow \]            \[\frac{9}{54}=\frac{4}{9}\Rightarrow g=24\] Substituting the values of b and g in (i), we get: \[18+24+w=54\Rightarrow w=12\] Hence, the jar contains 12 white marbles.


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