Finding the expected value of the net winnings and interpreting

Question

A player pays$7 to play a game. There are 12 red, 4 blue, 3 white, and 1 orange balls. A ball is picked at random. If a red ball is picked the player gets nothing. If a blue ball is picked the player gets $8. If a white ball gets picked the player gets $11. If an orange ball is picked the player gets $42. Find the expected value of the net winnings for the player and interpret.

Answer 1

The player should expect that there is a 

 

60% chance the player will get nothing

20% chance the player will get $8

15% chance the player will get $11

5% chance the player will get $42

 

Expected value = the probability of an option times the # of options

 

So the expected value of winning anything is 40% * 20 = 8 (minus the cost to play the games, so it is 1).

The expected value of winning $8 is -3.

The expected value of $11 is -4.

The expected value of $42 is -6.

 

So the interpretation is - don't waste your time on this game!

 

Hope this helps, Angelica.