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. ...

... b) Use your table to find the expected value of the game. ... 2. Use your table to find the expected value of the game. Answer. Expected value of the game, E (X) =. ...

... 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 ...

... Your net profit is. d) Find the expected value. ... Win $4999 0.0001 0.4999 Lose −$1 0.9999 −0.9999. So the expected value is a loss of 50 cents per game. ...

... Question 4. How much do you expect to gain? ... Use 3 decimal places.) c. Find the expected number of ... d. Find the standard deviation of the number of right-handers ...

... 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 ...

... deviate somewhat from the values we theoretically expect, so we ... This relative mag- nitude is found through division by the expected frequencies, as in ...

... 2. One evening, Fyodor decides to play 10 games of roulette, betting $100 on black each time (this bet ... (i) What is the expected value and ... (ii) Find the exact ...