Question

Each side of the square below is 8 inches. A triangle inside of a square. The top of the triangle divides a side of the square into 2 equal parts of 4 inches. The triangle is shaded and the area to the right of the triangle is shaded. What is the probability that a point chosen at random in the square is in the blue region? 0. 25 0. 33 0. 66 0. 75.

Answer 1

The probability that a point is chosen at random in the square is in the blue region is 0.8.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

As we know that the area of the shaded region is the sum of the area of triangle A and the area of triangle B. Therefore, the area of the blue shaded region is,

$\text{Area of shaded region} = (\dfrac{1}{2} \times 8 \times 8) + (\dfrac{1}{2} \times 4 \times 8)$

                                  $= (32) + (16)\\\\= 48\rm\ in^2$

The area of the square can be written as,

$\text{Area of Square} = \rm(Side)^2 = 8^2 = 64\ in^2$

Now, the probability that a point is chosen at random in the square is in the blue region can be written as,

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

$\rm Probability = \dfrac{\text{Area of blue region}}{\text{Area of square}}\\\\Probability = \dfrac{48}{60} = 0.8$

Hence, the probability that a point is chosen at random in the square is in the blue region is 0.8.

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