A person rolls a pair of six-sided dice, which are equally likely to come up any number from 1 to 6. If the person rolls a seven he gets $0. If he rolls any other number, he can choose either to win that amount or play the game again from the start. This person believes that the best strategy is to keep rolling until he gets a "high" number, so he wins a lot of money. However, he doesn't know what "high" number to pick.
Let's say he will stop rollling if he rolls a K or more, otherwise he will roll again.

Problem 1: What value of K maximizes his e-winnings?

a) 4
b) 6
c) 8
d) 10

Problem 2: What is the standard deviation of your distribution of his winnings, if he plays the correct K above?

a) $2.81
b) $3.32
c) $4.35
d) $5.17

Solution Summary

Expected return and standard deviation are calculated in the attached Excel file. Problem 1 and 2 are discussed in 82 words in the attached Word document along with the outcomes for the different die roles.

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Statistics: Probability of Die Rolls. A 6-sided die is rolled and depending on the result a ball is then chosen from one of three boxes. If the roll results in ...

... There are 6 outcomes of a die roll. Probability that 1 is rolled = 1/6 Probability that 3 is rolled = 1/6 Probability of rolling 1 or 3 = (1/6) + (1/6) = 1/3. ...

... In an Empirical approach to estimating or calculating probabilities the exact ... this empirical evidence our estimate of the probability that rolling this six ...

... It's clear enough that the odds of rolling a 1 are ... then, is the likelihood that I will roll a 1 ... need to solve this for any single-event probability, too -- not ...

... d) Find the probability that more than 5 of saplings ... for the calculation of expected value and binomial probabilities. ... random P(x) xP(x) variable) Rolling a 1 ...

... Data Simulation Discrete Probability Distribution Confidence Intervals. ... calculate the median for the 10 rolls of the ... 1. When rolling a die, is this an example ...

... What is the probability of rolling the number 4 (on one die) and the number 3 (on the other die) with a normal pair of dice if you roll the dice 100 times? ...

... 4. What is the probability of rolling 3 or higher on a die roll, if the roller has the option to re- - roll the die a single time? A) .66 B) .50 C) .75 D) .89. ...