Probability of an event is the measure of that event's chance of occurrence. The probabilities for the considered parts are:
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 the given case, we assume that Brenda always makes a hit in the square and not outside(so the probability of hitting inside the square becomes 1).
Now, we have sample space of point of hit as the points inside that square of side length 11 units.
Thus, S = points of square of 11 units side length,
A(S) = [tex]11^2 = 121 \: \rm unit^2[/tex]
E = hitting in the circle in the center of the square with diameter of 2 units.
A(E) = area of circle with diameter 2 = [tex]\pi(\dfrac{d}{2})^2 = \pi \times 1^2 = \pi \approx 3.14 \: \rm unit^2[/tex]
Thus, the probability of occurrence of event E (hitting inside the central circle) is:
[tex]P(E) \approx \dfrac{3.14}{121} \approx 0.025[/tex] (closer to 0 than 1)
Either Brenda hits on or inside the circle, or outside it in the white space of the box.
Thus, probability of Brenda hitting in white space of box =P(not hitting in the circle) = 1 - Probability of hitting in the circle [tex]\approx 1 - 0.025 \approx 0.975[/tex] (closer to 1 than 0)
Thus, the probabilities for the considered parts are:
Learn more about probability related to area here:
https://brainly.com/question/4138779
