To find the probability of losing a specific piece from the game, we first need to determine the total number of pieces and the specific conditions given in the question.
Understanding the Pieces
There are two types of shapes: triangles and squares.
- Triangles: 8 total (3 blue, 5 red)
- Squares: 10 total (6 blue, 4 red)
Total Pieces
The total number of pieces is:
Total = Triangles + Squares = 8 + 10 = 18
Calculating the Probabilities
We need to find the probability of losing:
- A blue triangle
- A red triangle
The probabilities are calculated as follows:
Probability of Losing a Blue Triangle
There are 3 blue triangles out of 18 total pieces:
P(Blue Triangle) = Number of Blue Triangles / Total Pieces = 3 / 18 = 1 / 6
Probability of Losing a Red Triangle
There are 5 red triangles out of 18 total pieces:
P(Red Triangle) = Number of Red Triangles / Total Pieces = 5 / 18
Final Probability Calculation
To find the probability of losing either a blue triangle or a red triangle, we add the two probabilities:
P(Blue Triangle or Red Triangle) = P(Blue Triangle) + P(Red Triangle) = (1/6) + (5/18)
To add these fractions, we need a common denominator:
P(Blue Triangle or Red Triangle) = (3/18) + (5/18) = 8/18 = 4/9
Result
The probability of losing either a blue triangle or a red triangle is 4/9.
