A bag contains 3 white, 5 black and 2 red balls, all of the same size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:
a red ball

Answer

To find the probability of drawing a red ball from the bag, we can follow these steps:

### Step 1: Identify the number of each color of balls in the bag.
- White balls: 3
- Black balls: 5
- Red balls: 2

### Step 2: Calculate the total number of balls in the bag.
To find the total number of balls, we add the number of white, black, and red balls together:
\[ \text{Total number of balls} = \text{Number of white balls} + \text{Number of black balls} + \text{Number of red balls} \]
\[ = 3 + 5 + 2 = 10 \]

### Step 3: Identify the number of favorable outcomes for drawing a red ball.
The number of favorable outcomes (the number of red balls) is:
\[ \text{Favorable outcomes} = 2 \quad (\text{since there are 2 red balls}) \]

### Step 4: Use the probability formula to find the probability of drawing a red ball.
The probability \( P \) of drawing a red ball is given by the formula:
\[ P(\text{Red ball}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P(\text{Red ball}) = \frac{2}{10} \]

### Step 5: Simplify the fraction.
To simplify \( \frac{2}{10} \):
\[ P(\text{Red ball}) = \frac{1}{5} \]

### Final Answer:
The probability of drawing a red ball from the bag is \( \frac{1}{5} \).

---