A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that a ball drawn from the bag at random will be neither red nor black?

Answer

To find the probability that a ball drawn from the bag at random will be neither red nor black, we can follow these steps:

### Step 1: Identify the number of each type of ball in the bag.
- Red balls (R) = 3
- White balls (W) = 5
- Black balls (B) = 7

### Step 2: Calculate the total number of balls in the bag.
Total number of balls = Number of red balls + Number of white balls + Number of black balls
\[ \text{Total} = R + W + B = 3 + 5 + 7 = 15 \]

### Step 3: Identify the favorable outcomes.
Since we want to find the probability of drawing a ball that is neither red nor black, we only consider the white balls.
- Number of favorable outcomes (white balls) = 5

### Step 4: Use the probability formula.
The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the event is drawing a white ball.
\[ P(\text{white ball}) = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{5}{15} \]

### Step 5: Simplify the fraction.
\[ P(\text{white ball}) = \frac{5}{15} = \frac{1}{3} \]

### Conclusion:
The probability that a ball drawn from the bag at random will be neither red nor black is \( \frac{1}{3} \).

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