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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

Respuesta :

The probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75

How to find the geometric probability?

When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:

  • E = favorable event
  • S = total sample space

Then:

[tex]P(E) = \dfrac{A(E)}{A(S)}[/tex]

where A(E) is the area/volume/length for event E, and similar for A(S).

For this case, we're given that:

  • We want to get probability for a randomly chosen  point in square to be in the blue region.
  • The diagram is attached below.

The favorable space is the blue shaded region.

The total sample space is the area of the considered square.

Let we take:

E = event of choosing point in the blue shaded region

Now, we have:

Area of blue region = Area of triangle with base = height = 8 inches + Area of right sided triangle which has base of 4 inch (look it upside down), and height of 8 inches

Area of blue region = [tex]\dfrac{1}{2} \times (8 \times 8 + 4 \times 8) = 48 \: \rm in^2[/tex]

Area of the square of sized 8 inches = 64 sq. inches.

Thus, we get:

[tex]P(E) = \dfrac{A(E)}{A(S)} = \dfrac{48}{64} = \dfrac{3}{4} = 0.75[/tex]

Thus, the probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75

Learn more about geometric probability here:

https://brainly.com/question/24701316