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 red ball

Answer

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

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

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

### Step 3: Determine the number of favorable outcomes for drawing a ball that is not red.
The favorable outcomes are the number of white and black balls combined.
\[ \text{Favorable outcomes} = \text{Number of white balls} + \text{Number of black balls} \]
\[ \text{Favorable outcomes} = 3 + 5 = 8 \]

### Step 4: Calculate the probability of drawing a ball that is not red.
Probability is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{8}{10} \]

### Step 5: Simplify the fraction.
\[ \text{Probability} = \frac{8}{10} = \frac{4}{5} \]

### Final Answer:
The probability that the ball drawn is not a red ball is \( \frac{4}{5} \).

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