One ball is picked up randomly from a bag containing 8 yellow,7 blue and 6 black balls , what is the probability that it is neither yellow nor black ?

Options

A. `3//4`
B. `4//7`
C. `2//9`
D. `1//3`

Explanation

To solve the problem of finding the probability that a randomly picked ball from a bag containing 8 yellow, 7 blue, and 6 black balls is neither yellow nor black, we can follow these steps:

### Step 1: Determine the total number of balls in the bag.
We have:
- Yellow balls = 8
- Blue balls = 7
- Black balls = 6

Total number of balls = Yellow + Blue + Black
= 8 + 7 + 6
= 21

### Step 2: Determine the number of favorable outcomes.
We are looking for the probability that the ball picked is neither yellow nor black. This means we are only interested in the blue balls.

Number of blue balls = 7

### Step 3: Calculate the probability.
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 picking a blue ball (neither yellow nor black).

So, the probability of picking a blue ball is:
\[ P(\text{Blue}) = \frac{\text{Number of blue balls}}{\text{Total number of balls}} = \frac{7}{21} \]

### Step 4: Simplify the probability.
Now, we simplify the fraction:
\[ P(\text{Blue}) = \frac{7}{21} = \frac{1}{3} \]

### Final Answer:
The probability that the ball picked is neither yellow nor black is \( \frac{1}{3} \).

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