Question

A die is tossed 5 times, getting an odd number is considered a success. Then the variance of the distribution of number of successes is

• A. \( \frac{8}{3} \)
• B. \( \frac{3}{8} \)
• C. \( \frac{4}{5} \)
• D. \( \frac{5}{4} \)

Hint:

For binomial distributions, use the formula \( \text{Variance} = n \cdot p \cdot (1 - p) \).

Answer 1

The Correct Option is B

Step 1: Recognize the Distribution
This is a binomial distribution problem, as the die is tossed 5 times with success defined as getting an odd number.
The probability of success (getting an odd number) is: \[ P(\text{success}) = \frac{3}{6} = \frac{1}{2} \] Thus, the probability of failure is also \( \frac{1}{2} \).
Step 2: Use the Variance Formula for Binomial Distribution
The variance for a binomial distribution is given by: \[ \text{Variance} = n \cdot p \cdot (1 - p) \] where \( n \) is the number of trials (5 in this case), and \( p \) is the probability of success.
Substituting the values: \[ \text{Variance} = 5 \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{5}{4} \]
Step 3: Conclusion
Thus, the variance of the distribution is \( \frac{5}{4} \).