Question

What is the variance of the number of times a 6 appears when a fair die is rolled 10 times?

Answer 1

Answer: $\dfrac{25}{18}$

Step-by-step explanation:

In Binomial distribution ,

The Formula to find Variance is given by :-

$\sigma^2=np(1-p)$ , where n = Total number of trials and p= probability of getting success in each trial.

Total outcomes on a fair dice (1,2,3,4,5,6)= 6

When we roll a fair dice, then the probability of getting a 6 =$\dfrac{1}{6}$

[∵ Probability = $\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}$]

Then, the variance of the number of times a 6 appears when a fair die is rolled 10 times :-

[ Here n= 10 and $p=\dfrac{1}{6}$ ]

$\sigma^2=(10)\dfrac{1}{6}(1-\dfrac{1}{6})\\\\=(10)\dfrac{1}{6}\dfrac{5}{6}=\dfrac{25}{18}$

Hence, the variance of the number of times a 6 appears when a fair die is rolled 10 times= $\dfrac{25}{18}$