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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... The variance (the standard deviation squared) is found by multiplying the expected number by the probability of not rolling a 2 on each roll (see http ...

...Die rolling An ordinary (fair) die is a cube with the ... Compute the probability of each of the following events: Event ... P (A) = P (B) = Solution: If we roll a die...

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 ...

Elementary Probability Theory: Rolling a Single Fair Die. ... a)do the probabilities add up to 1 ? c) What is the probability of getting of getting a number less ...

probability of rolling two dices. ... 2. Two balanced dice are rolled to see the number of dots facing ... Find the probability of observing a) Six dots on both the dice ...

... 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 ...

... a. The classical probability says that if we roll the dice for a very large number of times "two ... This post answers two simple problems in probabilities. ...

... 2) A standard 6-sided die is weighted so that the probabilities of rolling 2,3,4,5, or 6 are equal and the probability of rolling is 1 is twice the probably ...