Question

A die is continuously rolled until the total sum of all rolls exceeds 325. What is the probability that at least 95 rolls are necessary?

Answer 1

SOLUTION:

From given data,

A die is continuously rolled until the total sum of all rolls exceeds 325. What is the probability that at least 95 rolls are necessary

If at least 95 rolls are necessary , then the total of the first 94 rolls is at most 325.

Let be the result of roll i ,

E() = P() = (1+2+3+4+5+6) / 6 = 7/2

E() =7/2

E() = (1²+2²+3²+4²+5²+6²) / 6 = 91/6

Var () =  E() - [ E() ]²

Var () = 91/6 - [ 7/2]² = 35/12

Var () = 35/12