Mathematics
Grade10
Easy

Question

Brie designed a carnival game that involves tossing a beanbag into the box shown. In order to win a prize, the beanbag must fall inside the black rectangle. Find the probability of winning in a simplified form.

  1. fraction numerator straight x over denominator left parenthesis 6 straight x space plus space 6 right parenthesis end fraction
  2. fraction numerator straight x over denominator left parenthesis straight x space plus space 1 right parenthesis end fraction
  3. fraction numerator straight x over denominator left parenthesis straight x space plus space 6 right parenthesis end fraction
  4. fraction numerator straight x over denominator left parenthesis straight x space plus space 2 right parenthesis end fraction

hintHint:

In this question, we have to find the probability of winning in a simplified form, if Brie designed a carnival game that involves tossing a beanbag into the box shown and in order to win a prize, the beanbag must fall inside the black rectangle. As the length and breadth of black rectangle is x/2 and x and the length and breadth of the bigger box is (x+1) and 3x. Now we can easily the probability of winning i.e., the rato of area of black rectangle by total area of face of box.

The correct answer is: fraction numerator straight x over denominator left parenthesis 6 straight x space plus space 6 right parenthesis end fraction


    Probability of winning the prize
    fraction numerator Area space of space black space re c tangle over denominator Total space area space of space faceofbox end fraction
    equals fraction numerator straight x space space cross times space 1 half space straight x over denominator left parenthesis straight x space plus space 1 right parenthesis space 3 straight x end fraction
space equals space 1 half space cross times space fraction numerator straight x squared over denominator 3 straight x space left parenthesis straight x space plus space 1 right parenthesis end fraction
space equals fraction numerator straight x over denominator 6 space left parenthesis straight x space plus space 1 right parenthesis end fraction

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