Bob owns an aquarium with an unknown number of fish. One of these fish is red and the other 1 fish are black. Bob picks out one of these fish at random and finds that it is a black fish. He returns this fish to the aquarium and adds 8 more black fish, so that there are now + 8 fish (1 red fish and + 7 black fish). Then, he picks another fish at random and finds that it is the red fish.

What is the maximum likelihood estimate for , based on all information in the previous paragraph?