Questions: Mahjong is a strategy game for four players that is played using tiles. A typical set of Mahjong tiles includes 36 dot tiles, 16 wind tiles, and 12 dragon tiles. Clara places the dot, wind, and dragon tiles from a Mahjong set face down on a table. She chooses one tile at random. What is the probability that Clara chooses each type of tile? Probability of a dot tile: Probability of a wind tile: Probability of a dragon tile:

Solution Steps

To find the probability of choosing each type of tile, we need to determine the total number of tiles and then calculate the probability for each type by dividing the number of that type of tile by the total number of tiles.

1. Calculate the total number of tiles.
2. Calculate the probability of choosing a dot tile.
3. Calculate the probability of choosing a wind tile.
4. Calculate the probability of choosing a dragon tile.

To find the total number of tiles in the Mahjong set, we sum the number of each type of tile: \[ \text{Total Tiles} = \text{Dot Tiles} + \text{Wind Tiles} + \text{Dragon Tiles} = 36 + 16 + 12 = 64 \]

The probability of choosing a dot tile is calculated as follows: \[ P(\text{Dot Tile}) = \frac{\text{Dot Tiles}}{\text{Total Tiles}} = \frac{36}{64} = 0.5625 \]

The probability of choosing a wind tile is calculated as follows: \[ P(\text{Wind Tile}) = \frac{\text{Wind Tiles}}{\text{Total Tiles}} = \frac{16}{64} = 0.25 \]

The probability of choosing a dragon tile is calculated as follows: \[ P(\text{Dragon Tile}) = \frac{\text{Dragon Tiles}}{\text{Total Tiles}} = \frac{12}{64} = 0.1875 \]

Final Answer