What's the maximum amount you should pay to play a game?
You're playing a game where you have to throw a ball into a basket five times. You only have five tries. The probability of making the ball into the basket for any of the five tries is 60% or 6/10. If you make all five of the balls in, you win $1000. If you make four of the balls in, you win 500$. If you make three of the balls in, you win 100$. If you make one or two balls in, you get nothing. What's the maximum amount of money one should be willing to pay so that, given these certain probabilities, he or she will not risk losing any money?
This is just a hypothetical question I made up...
I think the answer must be over .6^5 x 1000. I'm not sure how to factor in the 2nd and 3rd prizes though, if they make much of a difference at all.
Note:I'm only a senior in high school and I think these types of question are at college level; if you could clearly explain how these types of questions are solved, that'd be great. I'm not very familiar with all the symbol lingo.