10th Class Mathematics Probability Question Bank Probability

  • question_answer In the given figure. JKLM is a square with sides of length 6 units. Points A and B are the mid-points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of \[\Delta JAB\]?  

    A)  5/8                        

    B)  7/8                   

    C)                     3/4                   

    D)         3/8                    

    Correct Answer: D

    Solution :

    Area of square JMLK \[={{6}^{2}}=36\text{ }sq.\]units     A and B are the mid-points of sides KL and LM. i \[\therefore \]   AL = KA = LB = BM = 3 units               Now, Area of \[\Delta ALB=\frac{1}{2}\times AL\times LB\]                         \[=\frac{1}{2}\times 3\times 3=\frac{9}{2}\,sq.\]units Area of \[\Delta JMB=\frac{1}{2}\times BM\times JM\]             \[=\frac{1}{2}\times 3\times 3=\frac{9}{2}sq.\] units. Area of \[\Delta KAJ=\frac{1}{2}\times KJ\times KA\]             \[=\frac{1}{2}\times 6\times 3=9\,sq.\]units Total area of all the three triangles             \[=\left( \frac{9}{2}+9+9 \right)=\frac{45}{2}\,\,sq.\] units \[\therefore \] Area of \[\Delta JAB=\left( 36-\frac{45}{2} \right)=\frac{27}{2}\] sq. units \[\therefore \]  Required probability \[=\frac{\frac{27}{2}}{36}=\frac{27}{2\times 36}=\frac{3}{8}\]

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