Answer:
Probability is 64%
Step-by-step explanation:
Given the smaller circle which is shaded whose radius is denoted by r and the largest circle whose radius is denoted by R
r = 3 inches
R = 5 inches
Step 1 : To calculate the area of shaded region.
Area of circle = [tex]\pi\cdot r^{2}[/tex]
⇒ Area = [tex]\frac{22(3)(3)}{7}[/tex]
= [tex]\frac{198}{7}[/tex] square inches
Step 2 : To calculate the area of larger circle.
Area of circle = [tex]\pi\cdot r^{2}[/tex]
⇒ Area = [tex]\frac{22(5)(5)}{7}[/tex]
= [tex]\frac{550}{7}[/tex] square inches
Step 3 : Calculate the probability that a point chosen from shaded region
Probability = Area of shaded region/Area of larger circle.
= [tex]\frac{198}{7}[/tex]/ [tex]\frac{550}{7}[/tex]
= [tex]\frac{198}{550}[/tex]
= 0.36 = 36%
Step 4 : calculate the probability that a point chosen inside the larger circle is not in shaded region.
Probability = 1 - 0.36
= 0.64 = 64%
Hence the probability is 64%
