Three faces of a fair dice are yellow, two are red and one is blue. Find the probability that the dice shows (a) yellow, (b) red and (c ) blue face.

Explanation

To find the probabilities of the different colored faces showing on a fair die with three yellow faces, two red faces, and one blue face, we can follow these steps:

### Step 1: Identify the total number of faces on the die
A standard die has 6 faces. In this case, the distribution of colors is:
- Yellow: 3 faces
- Red: 2 faces
- Blue: 1 face

### Step 2: Determine the total number of outcomes
The total number of outcomes when rolling the die is 6 (since there are 6 faces).

### Step 3: Calculate the probability of rolling a yellow face
The number of favorable outcomes for yellow is 3 (Y1, Y2, Y3).

Using the probability formula:
\[ P(\text{Yellow}) = \frac{\text{Number of Yellow Faces}}{\text{Total Number of Faces}} = \frac{3}{6} = \frac{1}{2} \]

### Step 4: Calculate the probability of rolling a red face
The number of favorable outcomes for red is 2 (R1, R2).

Using the probability formula:
\[ P(\text{Red}) = \frac{\text{Number of Red Faces}}{\text{Total Number of Faces}} = \frac{2}{6} = \frac{1}{3} \]

### Step 5: Calculate the probability of rolling a blue face
The number of favorable outcomes for blue is 1 (B).

Using the probability formula:
\[ P(\text{Blue}) = \frac{\text{Number of Blue Faces}}{\text{Total Number of Faces}} = \frac{1}{6} \]

### Summary of Results
- Probability of rolling a yellow face: \( P(\text{Yellow}) = \frac{1}{2} \)
- Probability of rolling a red face: \( P(\text{Red}) = \frac{1}{3} \)
- Probability of rolling a blue face: \( P(\text{Blue}) = \frac{1}{6} \)

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