Question

Alex challenged David to a free-throw duel. Alex and David would take turns shooting free throws until someone makes a shot. David makes free throws with probability 0.2. Alex makes free throws with probability 0.1. Assume independence.

Alex does like to complain. He says that he should have two attempts for each one of David's attempts since his success rate is half of David's. What is the probability that Alex is the first one to make a free throw with these rules? That is, the pattern of attempts is AADAADAAD… instead of ADADAD… in part (b).

I need exact answer.

Answer 1