We repeatedly throw a die, stopping when the value of the throw exceeds the value of the first throw. Compute the expectation value of the number of throws.

It is convenient to consider infinite sequences of die throws and then consider the subsequence of the subsequent entries starting from the first entry that satisfies the rules. So, if the sequence is 3, 2, 2, 1, 5, 2, 6,...., then the subsequence is 3, 2, 2, 1, 5, because the throw of 5 is the first one that is equal or larger than the first throw. The probability that under the rules you would have n die throws is thus the same as the probability that a subsequence has length n. The probability that the subsequence of a sequence starting with r has a length of n is:

p(r,n) = 1/6 * [(r - 1)/6]^(n-2) * (7- r)/6

The first factor of 1/6 is the probability that the first die throw yields r, the second factor is the probability of having n-2 die throws that are below r, the ...

Solution Summary

We solve this die throw problem from first principles. The value of the number of throws are given.

Question #1: Develop a program that prompts the user to guess the outcome of a diethrow. Then throw a die (using a random number generator) and inform the user if they guessed the correct outcome. Count the number of correct guesses. Develop the program using a separate class for the die. Your program should contain two separat

Please help with the following problem.
Compute the probabilities for each of the following when you throw five six-handed dice.
1) What is the probability that all five have different numbers?
2) What is the probability that at least four are the same?
3) What is the probability that exactly three are sixes?

The probability of throwing any two numbers on a die - say, either a 1 or a 2 - on a single throw is one chance out of three, or 33%.
When calculating the probability of repeating favorable throws with a single die the probability of throwing a 1 or a 2 twice in succession is 1/9, which is the square of one chance out of

If a die rolled one time, classical probability would indicate that the probability of a "two" should be 1/6. If the die is rolled 60 times and comes up "two" only 9 times, does this suggest that the die is "loaded"? Why or why not?
It is reported that about 35% of adults attend sports event during the previous year. W

Consider the following scenario to understand relationship between marginal and average values.
Suppose Tim is a professional basketball player, and his game log for free throws can be summarized in the table below. Fill in the columns to show Tim's free-throw percentage for each game and overall free-throw average.
Game

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 the probability of getting of getting a number less than

Constuct an unique pair of dice (6 sides) so that each of the sums 2 through 12 has an equal (nonzero i.e. cannot have two dice with all zero's) probability of occurring. The dice do not have to be identical.

You roll two fair dice, a green one and a red one.
a) Are the outcomes on the dice independent?
b) Find P(1 on green die and 2 on red die).
c) Find P (2 on green die and 1 on the red die).
d) Find P(1 on green die and 2 on red die) or (2 on green die and 1 on red die).