PLEASE lead me in the right direction!

#1
Here is the question that I can't seem to figure out!!! PLEASE HELP!! I've attached the JPEG of the question. This is my last question out of about 100 and I just can't seem to crack it.

($14 x .5) + (-$4 x .5) = $5 (this is what I get for the expected value but I know that isn't right!)

Just need help finding the expected value, then I think I can handle the rest. Thanks!
 

BGM

TS Contributor
#2
What does the value "0.5" means in your equation calculating the expectation?

What is the probability that you get two even numbers from two independent fair dice?
 
#3
What does the value "0.5" means in your equation calculating the expectation?

What is the probability that you get two even numbers from two independent fair dice?

.5 would be the probability that you would get an even number. That's how I read the problem. Am I wrong?
 
#5
Ok so the probability that you get two even numbers from two dice is 9/36 or .25. But then how to I attach the values to find the expected value?
 
#7
($14 x .25) + (-$4 x .75) ---- is this right?
Yes, that’s correct.

Another way to derive the probability of rolling two even numbers is to realise that the two dice are independent of one another. Each die has six possible outcomes of which three are even numbers. Thus, the probability of throwing an even number with one die is 3/6 = ½. For two dice, you have to throw an even number on die #1 and an even number on die #2. This probability is then ½×½ = ¼.

Okay, so the probability of winning $14 is ¼, and the probability of losing $4 is ¾. This means that on average, for every four games that you play, you will win one of them and lose the other three. Put in money terms, four games on average will win you $14 and lose you 3×$4 = $12, so you can expect to gain $2 for every four games played. But $2 is for four games, and therefore your expectation for a single game is E = $2/4 =$0.5. If you go over this explanation carefully, you will hopefully see that it is arithmetically exactly equivalent to E = ¼×$14 + ¾×(–$4).