Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Ask your questions and receive precise answers from experienced professionals across different disciplines. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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

Sagot :

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

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.