Answer:
The probability that a point chosen at random will be in the shaded region is 0.25
Step-by-step explanation:
We have been given a small shaded circle inside a larger un-shaded circle. This is shown in the image attached below.
The area of smaller circle is 78.5 squares inches and the area of larger circle is 314 square inches. We have to find the probability that a point chosen at random will be in the shaded region.
Probability is defined as the ratio of Favorable outcome to the Total outcomes. In this case the favorable outcome is that the point should be inside the shaded region i.e. in an Area of 78.5 square inches. And the total outcome is that the point can be anywhere inside the larger circle i.e. within an Area of 314 square inches. Thus the probability that a point chosen at random will be inside the shaded region will be:
[tex]Probability = \frac{\text{Favorable Outcome}}{\text{Total Outcome}} \\\\ = \frac{78.5}{314}\\\\=0.25[/tex]
Thus, the the probability that a point chosen at random will be in the shaded region is 0.25. This means there is a 25% chance that a randomly chosen point will be inside the shaded region.
