A college basketball player makes 80% of her free throws. suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. the expected number of free throws required until she makes her first free throw of the season is

Let n be the number of expected free throw until she makes the first throw. 

Suppose the number of throws are 10, Then she will make 8 of the 10 throws. On 5 throws, she make 4 (80% of 5) and on 2 throws, she makes 1.6, it means one throw. We deduce that the expected number of free throws until she makes one is 2.