Every time before drawing a marble he guesses the color of the marble he will draw.
He decides to always guess the color that occurs most frequently remaining in the bag (if there is a tie, he chooses either color).
Find the expected number of correct guesses.
Find a formula for the number of correct guesses for starting with X black and Y white marbles.
This problem is a modified version of Guessing suit and addresses an interesting question that came up in the comments.