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

Hint:

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

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.