Large deviation theory exercise

Question

I would appreciate some hints on this problem: a die is thrown ten times, use large deviation function of a Bernoulli distribution to give an estimate of the probability that the sum is 27. First it seems to me this is not a sequence of Bernoulli variables and second assuming it is how to scale the mean to be between 0 and 1?

Answer 1

I think I got it: an estimation can be thought as replacing the sum of 10 independent variables by a single Bernoulli variable and scale appropriately the approximation given by the large deviation function.