The mean of binomial distribution `B(4, (1)/(3))` is

Options

A. `(1)/(3)`
B. `(2)/(3)`
C. `(4)/(3)`
D. 4

Answer

To find the mean of the binomial distribution \( B(4, \frac{1}{3}) \), we can use the formula for the mean of a binomial distribution, which is given by:

\[ \text{Mean} = n \cdot p \]

Where:
- \( n \) is the number of trials
- \( p \) is the probability of success on each trial

### Step 1: Identify \( n \) and \( p \)

From the given binomial distribution \( B(4, \frac{1}{3}) \):
- \( n = 4 \)
- \( p = \frac{1}{3} \)

### Step 2: Substitute \( n \) and \( p \) into the mean formula

Now, we can substitute the values of \( n \) and \( p \) into the mean formula:

\[ \text{Mean} = 4 \cdot \frac{1}{3} \]

### Step 3: Calculate the mean

Now, we perform the multiplication:

\[ \text{Mean} = \frac{4}{3} \]

### Conclusion

Thus, the mean of the binomial distribution \( B(4, \frac{1}{3}) \) is:

\[ \text{Mean} = \frac{4}{3} \]

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