Question

You roll 36 fair dice. How many ones do you expect to get?

Answer 1

We roll 36 dice  so, n =36

Now in rolling a dice we get following outcomes

S= {1,2,3,4,5,6}

Now Probability of getting one in rolling a dice (P) = 1/6

Let getting one in rolling a dice is a success than

P(success) =1/6

P(failure) = 1-1/6 = 5/6

which follows bernoulli distribution with probability of success = 1/6

Now if we roll 36 dice then using approximation

We get a binomial distribution with parameter

n =36, p = 1/6

q=1-p = 5/6

Now , according to question we are calculating expected number of ones in 36 dice

Let X denotes the number of ones in 36 fair dice roll.

then X ~ Binomial(36,1/6)

Now,

E[X] = np

= 36*1/6

= 6 Answer

We expect to get 6 ones in rolling 36 fair dice.