probability

Question

You and some of your friends decide to visit the Eastern Idaho state fair. One of your friends comes to you and says that he wants you to play this new game he found. He says he just played it and won $10 after playing 3 times.

Here are the game rules:
You just pay $2.75 to start the game and spin a big spinner. Whichever number it lands on, you get that much money back. The spinner has four sections labeled 1, 2, 3 and 4 each is a different size. See the picture below of what the spinner looks like.

You just finished taking FDMAT108 and remember learning about the expected value. You quickly calculate the expected value before you decide whether you will play or not. You find the probabilities of landing on each number and record them in a nice little table seen below.

 

Spinning Probabilities
Land on Number Probability
1 0.380
2 0.259
3 0.202
4 0.159


What would your expected earnings on average be per game?

 

About how much should you expect to win (or lose) if you played 100 times?

Answer 1

Expected value is evaluated by summing: the products of (1) the chance of each event and (2) the net gain of each event.

 

(1-2.75)*0.380+(2-2.75)*0.259+(3-2.75)*0.202+(4-2.75)*0.159 =

1*0.380+2*0.259+3*0.202+4*0.159-2.75 = -0.61

 

Each round the expected earning would be -0.61 dollars.

So, if you play 100 times you expect to lose about 61 dollars.