A target is constructed of a 6 ft diameter circular piece of plywood, on which a 2 ft diameter circle was painted. If a person is blindfolded, randomly throws a ball and hits the target, what is the probability they also hit within the smaller circle?

The probability of the dart hitting the inner circle is 11.2 %.

Step-by-step explanation:

To solve this problem we first need to find the area of the whole target and the area of the smaller target. Since they're both circular, their area is given by the formula:

area = pi*r²

For the whole target:

area target = pi * (6/2) ² = 28.26 ft²

For the inner target:

area inner = pi * (2/2) ² = 3.14 ft²

The probability that the dart will hit the inner area is:

p = area inner / area target = 3.14 / 28.26 = 0.112

The probability of the dart hitting the inner circle is 11.2 %.