Probability : 20 points
a carnival game requires the contestant to throw darts at balloons attached to a board. each balloon has a radius of 3 cm, and the board measures 1 m by 1 m. how many balloons are needed for a player to have a theoretical probability of 0.25 of winning? assume that the darts are thrown randomly and that all darts hit the board.
i know how to get the answer using formulas for area, but i need to somehow use probability?

The number of balloons needed is 64

Step-by-step explanation:

Let's consider that each balloon has a radius of 3 cm, so the  total diameter of a balloon is 6 cm.

The board measures 1 m x 1 m, with that we can calculate how many balloons fits in the left side of the board.

100 cm ÷ 6 cm = 16,66 Total of 16 balloons in one side.

The same applies to the upper side of the boards with 16 balloons as well.

Multiplying both sides we can find the maximum amount of balloons that can be possibly be put on the board.

16 x 16 = 256

Total of 256 balloons covering the entire board.

Considering the theoretical chance of winning being 0.25  which equals to 25% of something to happen, we need to calculate how many balloons would cover 25% of the board, that can be easily calculate in this way:

If 256 balloons is 100%, since it covers the whole board, we can divide it by 100 to get a 1% value and multiply it by 25, and find the number of balloons that will mach the 0.25 probability.  

256 ÷ 100 = 2,56 (This is 1%)

2,56 x 25 = 64

64 Is the total amount of balloons  necessary to have a 0.25 probability of winning assuming that the darts are thrown randomly.