Option D - about 80% is the answer
Step-by-step explanation:
Step 1 :
Let L be the length of the square
Since the 2 semi circles are drawn with side of the square as diameter , the diameter of the 2 shaded semicircles is L
Hence the radius = [tex]\frac{L}{2}[/tex]
Step 2 :
The total outcome = the point is inside the square = area of the square = L²
The favorable outcome is that the point is inside the shaded area = Area of 2 shaded semi circles of radius L/2 = [tex]\pi[/tex] × [tex](\frac{L}{2}) ^{2}[/tex] = [tex]\pi[/tex] × [tex]\frac{L}{4}[/tex]
The probability that the point is inside the shaded area = favorable outcome ÷ the total outcome
= ([tex]\pi[/tex] × [tex]\frac{L}{4}[/tex]) ÷ L² = [tex]\frac{\pi }{4}[/tex] = [tex]\frac{3.14}{4}[/tex] = 0.785
Converting this into percentage it give 78.5% which is about 80%
Step 3 :
Answer :
Option D - about 80% is the answer
