Question

calculating expected value using a table
hanita created a game for the school fair. each game costs $5. the player is shown a jar filled with different colored marbles. then the jar is hidden from view and well shaken so the player cannot see the colors of the marbles and so the marbles are distributed randomly. then the player draws a marble.
the table below shows the colors of the marbles in the jar, the probability of selecting the color, and how much is won by the player selecting a marble of that color.
complete the table by computing the amounts indicated in the top row, and then answer the remaining questions to find the expected value of the game for the player.
note: if the player wins less than the $5 they pay, then they will lose money. this means the total winnings will be written as a negative number.
to find the expected value of the game for the player, compute
the sum of all the values in the probability × total winnings column.
expected value of game = $
round your answer to the nearest cent
question help: video read message instructor

Explanation:

Step1: Calculate Total Winnings for each color

• For white: \(0 - 5=-5\)
• For pink: \(8 - 5 = 3\)
• For red: \(5 - 5=0\)
• For purple: \(12 - 5 = 7\)
• For silver: \(2 - 5=-3\)

Step2: Calculate Probability × Total Winnings for each color

• For white: \(0.39\times(- 5)=-1.95\)
• For pink: \(0.07\times3 = 0.21\)
• For red: \(0.11\times0=0\)
• For purple: \(0.04\times7 = 0.28\)
• For silver: \(0.39\times(-3)=-1.17\)

Step3: Calculate the expected value

Sum up the values in the Probability × Total Winnings column: \(-1.95+0.21 + 0+0.28-1.17=-2.63\)

Answer:

The Total Winnings for white is \(-5\), Probability × Total Winnings for white is \(-1.95\); Total Winnings for pink is \(3\), Probability × Total Winnings for pink is \(0.21\); Total Winnings for red is \(0\), Probability × Total Winnings for red is \(0\); Total Winnings for purple is \(7\), Probability × Total Winnings for purple is \(0.28\); Total Winnings for silver is \(-3\), Probability × Total Winnings for silver is \(-1.17\). The expected value of the game is \(-2.63\)