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Hello professor,

I also need help with question number 45 from the mixed review from chapter 4. It starts like this "Your campus newspaper decides to run a raffle..."

Hi Katherine,

Here is the question: Your campus newspaper decides to run a raffle that has relatively good odds. The raffle involves paying \$5 to draw a single colored marble from a bag. The bag contains 2 red, 6 white, 18 blue, and 54 yellow marbles. If the participant selects a red marble, he/she is given \$25. If a white marble is drawn, he/she gets \$7. If a blue marble is selected, he/she gets \$5, and if a yellow marble is selected, he/she is given \$4. What is the expected value for a single raffle drawing?

To answer this problem, you might want to set up a table, but before we do that let's mention some important ideas. The game requires us to pay \$5 just to play, so we start out at a loss. This means if we select a red marble, we only net \$20 in profit. That is because we paid \$5 to have the right to select a marble. If we draw a yellow marble, we end up losing a dollar because we are only paid \$4 for the yellow marble, yet it cost us \$5 to play. Lastly, there are a total of 80 marbles in the bag. This means that the probability of drawing a red marble = # of red marbles/ total number of marbles = 2 / 80. These ideas should help you understand the table below.

 Outcome X (Net \$ Amount Lost or Gained) P(X) red 20 2/80 white 2 6/80 blue 0 18/80 yellow -1 54/80

Then, we multiply the x column by the P(x) column and add the results to find the mean:

 Outcome (marble color) X (Net \$ Amount Lost or Gained) P(X) X*P(X) red 20 2/80 40/80 white 2 6/80 12/80 blue 0 18/80 0 yellow -1 54/80 -54/80 -2/80 = -0.025

I hope that helps,

Professor McGuckian