On three rolls of a single die you will lose $10 if a 5 turns up at least once, and you will win $7 otherwise. What is the expected value of the game?

Solution Preview

First we should calculate the probability that you roll a die 3 times and no 5 comes up. Each toss of the die has a probability of 5/6 of NOT being a 5. So,

P(3 rolls and no 5) = (5/6)^3 = .5787.

This immediately tells us the probability that we will roll at least one 5, out of three rolls. It is simply the following

P(3 rolls and at least one 5) ...

Solution Summary

A step-by-step solution is provided which covers the process of finding the expected value of a game.

... d. Find the expected value (Round to the nearest hundredth as needed) e. If you ... a. The pick 3 game is a better bet because it has a larger expected value. ...

... Can we conclude that the mean time for a game is less than 3.50 hours? ... Use the .05 significance level. Hint: To find the expected frequencies use the ...

... return or loss for each type of game and level ... their gambling plan, and what is their expected loss for ... Basically, I used excel solver to find the solution for ...

...Find the total interest paid over the life of the loan ... In the game Over-and-Under, a pair of dice is ... Determine a person's expected net winnings if the bet is as ...

... value of the infinite sum of its expected current and ... At [250, 300], both players can expect the other one to ...game, so whatever discount rate we find for one ...

... Since the expected value is a negative answer, we should say that the game is not ... Find the probabilities that the sample contains exactly 3 defective screws ...

... When equating these formulae to find p and q, we get what was expected: a Nash equilibrium is to ... I hope this helps! Questions in game theory are assessed. ...