In a binomial distribution, the occurrence and the non-occurrence of an event are equally likely and the mean is 6. The number of trails required is:

Options

A. 15
B. 12
C. 10
D. 6

Answer

To solve the problem step by step, we need to understand the relationship between the mean of a binomial distribution, the number of trials, and the probability of success.

### Step-by-Step Solution:

1. **Understanding the Binomial Distribution**:
In a binomial distribution, the mean (μ) is given by the formula:
\[ \mu = n \cdot p \]
where:
- \( n \) = number of trials
- \( p \) = probability of success on each trial

2. **Given Information**:
- The occurrence and non-occurrence of an event are equally likely, which means:
\[ p = 0.5 \quad \text{and} \quad q = 0.5 \]
- The mean (μ) is given as 6.

3. **Substituting the Values into the Mean Formula**:
We can substitute the known values into the mean formula:
\[ 6 = n \cdot 0.5 \]

4. **Solving for n**:
To find \( n \), we can rearrange the equation:
\[ n = \frac{6}{0.5} \]
Simplifying this gives:
\[ n = 6 \times 2 = 12 \]

5. **Conclusion**:
Therefore, the number of trials required is:
\[ n = 12 \]

### Final Answer:
The number of trials required is **12**.

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