Question

A die is rolled repeatedly until the sum of the numbers obtained islarger than 200. What is the probability that you need more than 66 rolls to do this?Hint: If X is the number of dots showing on the face of a die, E[X] = 7/2 and Var(X)= 35/12.

Answer 1

A bit theory

solution

A die is rolled repeatedly until the sum of the numbers obtained is larger than 200. Now in order to obtain the probability that we need more than 66 rolls to do this let us assume that be outcome of the die on consecutive rolls. Note that as it is given if X is the number of dots showing on the face of a die, E[X] = 7/2 and Var(X)= 35/12.

Note that if for any given N=n,

then

Let N be the number of roll that is needed to obtain the sum of the numbers larger than 200

So then probability that we need more than 66 rolls to do this

Hence the answer...............

Thank you..........