Question

10. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded.

about 5%
about 10%
about 20%
about 25%​

Answer 1

about 20%

Explanation:

The ratio of the area of an inscribed circle to that of its enclosing square is π : 4. That doesn't change for this figure, as when ratios are multiplied, in this case by 4, they stay the same (see the attached image).

π : 4 is about

3.14 : 4,

which can be multiplied by 25 to get:

78.5 : 100,

the approximate probability that any random point lands within one of the circles. To get the negative probability (the chance of the point NOT landing on the shaded circles), simply subtract the above ratio from 1.

100 : 100 ← 1

- (78.5 : 100)

21.5 : 100

So, the probability that the point lands in the non-shaded region of the square is 21.5 : 100, or 21.5%, and this can be rounded down to 20%.

Answer 2

about 20%

Explanation:

diameter of 1 circle = 2r

radius of 1 circle = r

area of 1 circle = πr²

area of 4 circles = 4πr²

side of square = 2 × 2r = 4r

area of square = (4r)² = 16r²

unshaded area = 16r² - 4πr²

approximate unshaded area = 3.433r²

p(unshaded area) = 3.433r² / 16r²

p(unshaded area) = 3.433/16 = 0.2146 = 21%

Answer: abour 20%