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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
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