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:
not a black ball

Answer

To find the probability that the ball drawn is not a black ball, we can follow these steps:

### Step 1: Determine the total number of balls in the bag.
- The bag contains:
- 3 white balls
- 5 black balls
- 2 red balls

**Total number of balls = Number of white balls + Number of black balls + Number of red balls**
\[ \text{Total number of balls} = 3 + 5 + 2 = 10 \]

### Step 2: Determine the number of favorable outcomes.
- We need to find the probability of drawing a ball that is **not black**.
- The balls that are not black are the white and red balls.

**Number of non-black balls = Number of white balls + Number of red balls**
\[ \text{Number of non-black balls} = 3 + 2 = 5 \]

### Step 3: Calculate the probability.
- The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes is the number of non-black balls (5), and the total number of outcomes is the total number of balls (10).

\[ \text{Probability of not drawing a black ball} = \frac{5}{10} = \frac{1}{2} \]

### Final Answer:
The probability that the ball drawn is not a black ball is \(\frac{1}{2}\).

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