200k views
1 vote
A 3 ft by 5 ft wooden board has three equally sized circles cut out of it. A penny will be randomly tossed onto the board. What is the probability the penny will fall through any of the holes?

User Cocoafan
by
5.0k points

1 Answer

6 votes

Answer:

Pr = 15.71% ≈ 16%

Explanation:

Let's begin by listing out the data given unto us, we have:

Length of board = 3 ft, Width of board = 5 ft,

Area of board = Length * Width = 3 * 5 = 15 ft²,

Diameter of each circle (d) = 1 ft; r = d ÷ 2

⇒ r = 1 ÷ 2 = 0.5 ft

Area of each circle = πr² = π * 0.5² = 0.785 ft²

Area of the three circles = 3πr² = 2.356 ft²

Probability = favourable outcome ÷ Total outcome

Probability of the penny falling into the hole = area of the three circles ÷ area of board

Pr = 2.356 ÷ 15 = 0.1571

Converting to percentage, we multiply by 100

Pr = 0.1571 * 100

Pr = 15.71% ≈ 16%

Therefore, the probability of the penny falling into the hole is 15.71% ≈ 16%

User Marol
by
4.9k points