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.

Use a worksheet to simulate therolling of dice. Use the VLOOKUP function to select the outcome for each die. Place the number for the first die in column B and the number for the second die in column C. Show the sum in column D. Repeat the simulation for 1000 rolls of the dice. What is your simulation estimate of the probabilit

Dierolling
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute t

Calculate the following probabilities:
a) Flipping "heads" with a normal coin five times in a row.
b) Rolling a "6" with one die.
c) Rolling a "7" with two dice.
d) Drawing a jack OR a red card (with replacement).
e) Drawing an ace, followed by a king (with replacement).

Question 3
An experiment consists of rolling one die. Let A be event that thedie shows more than one, B be event that thedie shows more than 4, and C be event that die shows an even number.
a) List the sample space of this experiment.
b) Find P(A), P(B), P(C)
c) Find P(A or C), P(A or B), P(A and C), P(B and C)
d) A

Can you help me understand how to solve this problem? (I need the process and math behind it, not just the answer).
Suppose I have a 10-sided die. It's clear enough that the odds of rolling a 1 are 10% for any single roll. What, then, is the likelihood that I will roll a 1 given 10 rolls? Given 5 or 20 rolls?
I'd need to sol

See attached file for complete problem set.
1. Find theprobability of obtaining three heads.
2. What is theprobability that he will be at his starting point after three flips of the quarter?
3. What is the expected number of 1's?
4. What is the standard deviation of the number of 2's?

a) If you roll a single fair die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?
b) Assign probabilities to the outcomes of the sample space of part? a)do the probabilities add up to 1 ?
c) What is theprobability of getting of getting a number less than

1. (a) Roll a 6-sided die and then flip a coin the no. of times shown by thedie. Letting Y be the no. of these flips coming up heads. What is E[X] and var(X)?
(b) Repeat part a assuming first rolling two dice.