Reviewing movies


#1

Roger reviews movies and gives each movie independently either a thumbs up with probability p or a thumbs down with probability q=1-p.let α be the expected number of reviews before both at least n thumbs ups and at least m thumbs downs are given. Let β be the expected number of reviews before either at least n thumbs up or at least m thumbs down are given

with n=3 and m =7 find the value of p for which the difference α-β is the smallest and give your answer as 1000 p, rounded to nearest integer.