Answer: [tex]\dfrac{25}{18}[/tex]
Step-by-step explanation:
In Binomial distribution ,
The Formula to find Variance is given by :-
[tex]\sigma^2=np(1-p)[/tex] , 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 =[tex]\dfrac{1}{6}[/tex]
[∵ Probability = [tex]\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]]
Then, the variance of the number of times a 6 appears when a fair die is rolled 10 times :-
[ Here n= 10 and [tex]p=\dfrac{1}{6}[/tex] ]
[tex]\sigma^2=(10)\dfrac{1}{6}(1-\dfrac{1}{6})\\\\=(10)\dfrac{1}{6}\dfrac{5}{6}=\dfrac{25}{18}[/tex]
Hence, the variance of the number of times a 6 appears when a fair die is rolled 10 times= [tex]\dfrac{25}{18}[/tex]
The variance of number is [tex]\frac{25}{18}[/tex]
To understand more, check below explanation.
The variance is computed as,
[tex]\sigma^{2} =n*p*(1-p)[/tex]
Where, n is number of trials, p is probability of success.
When a die is rolled, Probability of getting 6 [tex]=\frac{1}{6}[/tex]
Since, fair die is rolled 10 times i.e. n = 10 and p= 1/6
[tex]\sigma^{2} =n*p*(1-p)\\\\\sigma^{2} =10*\frac{1}{6} *(1-\frac{1}{6} )\\\\\sigma^{2} =\frac{50}{36}=\frac{25}{18}[/tex]
Hence, the variance of number is [tex]\frac{25}{18}[/tex]
Learn more about the variance here:
https://brainly.com/question/25639778
