STEP II 2007 question 12 solution

TSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP II 2007 question 12 solution

(i) First observe that p(first six after r throws of a single die) = .

P(stop after r throws) = p(no sixes in first r-1 throws and 2 sixes on rth throw) + p(no sixes in k-1 throws, single six after k throws and 2nd six on rth throw (i.e. r-k throws of single die))

Then E(T) =

.

So if E(T)=m, we have

.

Since we need the -ve root, and so we end up with .

Solution by DFranklin.