Question

A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

A.) about 90%
B.) about 70%
C.) about 60%
D.) about 80%

Answer 1

Option D - about 80% is the answer

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 =
`(L)/(2)`

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 =
`\pi` ×
`((L)/(2)) ^(2)` =
`\pi` ×
`(L)/(4)`

The probability that the point is inside the shaded area = favorable outcome ÷ the total outcome

= (
`\pi` ×
`(L)/(4)`) ÷ L² =
`(\pi )/(4)` =
`(3.14)/(4)` = 0.785

Converting this into percentage it give 78.5% which is about 80%

Step 3 :

Answer :

Option D - about 80% is the answer