Q: Expected Value of Balls Drawn Until a Yellow is Drawn You are playing a game in which you draw randomly from a bag containing 3 red balls, 2 blue balls and a single yellow ball. The ball is not replaced after each draw, and they are all equally likely to get selected. The red ball is worth \$3, the blue ball is worth \$5 and the yellow ball is worth \$25. In each case below the random variable X associated with the outcome is the value of the balls drawn.
Supposed you are allowed to keep drawing balls until you get the yellow ball. What is the expectation of X for balls drawn? 
I know you can only draw a maximum of 6 times, but I am having trouble setting up the problem. 

A: Hint.  Each red or blue ball has a $50$-$50$ chance of being drawn before the yellow ball.  So for one specific red ball, its expected value to you is
$$\frac12\times3+\frac12\times0\ .$$
Can you finish the problem from here?

A: By symmetry, you will expect to draw half of the non-yellow balls before the yellow ball and the other half after. Half of the non-yellow balls are worth $\$4.50+\$5.00=\$9.50$, and with the yellow ball, your expected winning is $\$25+\$9.50$=$\$34.50$.
