A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at random from the bag. Find the probability that the balls drawn is
neither white nor black

Answer

To find the probability that the ball drawn is neither white nor black, we can follow these steps:

### Step 1: Determine the total number of balls in the bag.
We have:
- White balls = 5
- Red balls = 7
- Black balls = 4
- Blue balls = 2

Total number of balls (N_t) = 5 + 7 + 4 + 2 = 18.

### Step 2: Identify the favorable outcomes.
We need to find the probability of drawing a ball that is neither white nor black. This means we are interested in red and blue balls only.

Number of red balls = 7
Number of blue balls = 2

Total favorable outcomes (N_f) = Number of red balls + Number of blue balls = 7 + 2 = 9.

### Step 3: Calculate the probability.
The probability (P) of drawing a ball that is neither white nor black is given by the formula:

\[ P(\text{neither white nor black}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:

\[ P(\text{neither white nor black}) = \frac{9}{18} = \frac{1}{2} \]

### Final Answer:
The probability that the ball drawn is neither white nor black is \( \frac{1}{2} \).

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