Answer:
The number of balloons needed is 64
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.