if you spin and land on a 1 you get $3,

Question

if you spin and land on a 1 you get $3, if you spin and get a 2 you get $5, if you spin and get a 3 you win $4. If you land on a 4 you pay $10, what is the expected value?

Answer 1

"In probability theory, the expected value of a random variable is intuitively the long-run average value of repetitions of the experiment it represents." -- Wikipedia

 

In the long run, the experimental probability "is expected" to resemble the theoretical probability.  In this problem, 1/4 of the time, you will land on each of the numbers 1-4 if it is a "fair" spinner (that is, each number has an equal probability of occurring).

 

Let x = the number of times that you spin

Let y = the expected value that you spend/receive

 

For each number, the value received is (1/4)*(individual value/cost)

    (1/4)x*3 + (1/4)x*5 + (1/4)x*4 - (1/4)*10 = (1/1)xy

 

     3x + 5x + 4x -10x = 4xy      [re-write; multiply by 4]

         2x = 4xy                    [collect terms]

          1/2 = y                    [divide both sides by 4x]

This game favors the player; the player expects to average $0.50 on each spin.

To change this, the player must pay at least $0.50 to take each spin.