A large wooden floor is constructed with wood-planks which are 2 inches wide. A uniform circular disk of diameter 2.25 inches is dropped at random on the floor. What is the probability that the disk touches three of the wood-planks? Give your answer as a decimal rounded to four places (i. e. X.).

Step-by-step explanation:

The side length of each wooden plank is 2 inches.

Area of each wooden plank is

Area = 2² = 4 inches²

Area of 3 wooden planks is 3 × 4 = 12 inches²

The formula for determining the area of the circular disc is expressed as

Area = πr²

π = 3.14

Radius, r = diameter/2 = 2.25/2 = 1.125 inches

Area of circular disc = 3.14 × 1.125² = 3.974

Probability is expressed as

Number of favorable outcomes/number of total outcomes

Therefore, the probability that the disk touches three of the wood-planks is

3.974/12 = 0.3312

72 is the answer to this problem