A total of 30 bears-consisting of 10 red bears, 10yellow bears, and 10 blue bears-are randomly arranged in a bucket. A child begins grabbing the bears at random, with all selections equally likely. The bears are selected "without replacement," i.e., she never puts the bears back after she grabs them.
How many bears does the child expect to grab before the first red bear appears? (Please do not include the red bear itself; only include the bears that appear strictly before the first red bear appears.)