Given:
Length of one side of the square = 12 units.
We have the following:
Area of the square = 12 x 12 = 144 square units
Area of the shaded region.
The shaded region forms a right triangle with the dimensions:
height = 8 units
Base = 11 units
The area will be:
[tex]\frac{1}{2}*8*11=44\text{ square units}[/tex]The area of the shaded region is 44 square units.
• Part d:
The probability that a randomly chosen point is in the shaded region.
To find the probability, apply the formula:
[tex]\begin{gathered} P(shaded)\text{ = }\frac{Area\text{ of shaded region}}{Area\text{ of square}} \\ \\ =\frac{44}{144} \\ \\ =\frac{11}{36} \end{gathered}[/tex]The probability that a randomly chosen point is in the shaded region is 11/36.
• Part e.
The probability that a randomly chosen point will not land in the shaded region.
To find the probability, apply the formula:
[tex]\begin{gathered} P(not\text{ shaded\rparen = 1 - P\lparen shaded\rparen} \\ \\ =1-\frac{11}{36} \\ \\ =\frac{36-11}{36} \\ \\ =\frac{25}{36} \end{gathered}[/tex]Therefore, probability that a randomly chosen point is not in the shaded region is 25/36.
• Part F.
What is the probability that any point randomly selected will land on a specific point.
The probability that any point randomly selected will land on a specific point will be:
[tex]\frac{1}{144}[/tex]Now, the probability that any randomly selected point will land on a specific line will be:
[tex]\frac{1}{144}[/tex]ANSWER:
• d. 11/36
,• e. 25/36
,• f. 1/144
