Amusement Park Game

You are given the chance to win a large stuffed animal for hitting one of the red dots on a large board with a paintball gun. The board is 6 feet wide by 4 feet high. The red dots are 3 inches in diameter. The paintballs are .25 inches in diameter. A dot is considered to be hit if any part of the pain touches it. There are 60 red dots spaced randomly around the board. What is the probability of winning the stuffed animal?

My Work: 1 paintball covers .049 sq inches. The 60 red dots cover a total of 424.115 sq. inches. The board covers a total 3456 sq. inches. The probability is something over 3456 sq. inches? Since the paintball has to touch any part of a dot, the total area of the dots has to be added to the paintball area? HELP! Thanks.

"Probability" is measured in fractions or (more usually) percentages; you should not have obtained an answer in terms of square inches.

Please reply showing the rest of your work and reasoning, and clarifying how many paintballs the customer gets in one game.

Thank you.

Eliz.

The answer is to be in fraction form. sq inches/sq inches cancels out and your left with just the numbers. I did show my work with out all the pi r^2 and converting ft. to inches. I am stuck as to how to figure the amount of possible space that could win you an animal. very frustrated because I was told I'm heading in the right direction. Where do I go from here? Thanks.

How many paintballs does a player get in a game? How big a dot does the paintball make? (Being hard, it seems reasonable to assume that the ball will make a smaller mark than its diameter. Unless it's a breakable ball, in which case the splash will likely be bigger.)

Thank you.

Eliz.

ASSUMING:
1: required is probability with only 1 shot
2: probability that the 4 by 6 board is hit is 100%
3: a paintball makes a circle of exactly its size, so diameter .25 inch

Since "A dot is considered to be hit if any part of the paint touches it",
then we can say that the paintball must be fully inside a dot of diameter
3.5 inches, since the .25 inch ball can be at most tangent to the 3 inch dot.

Then prize winning area = pi * 1.75^2 * 60 = ~577.268

So probability = ~577.268 / 3456 = ~.167 : about 167 out of 1000