# roll

1. ### Fair dice roll. The expected payoff?

Consider the following game: Two fair dice are rolled. If the sum is 7, you win $10. If the sum is 11, you lost$ 20. What is the expected payoff for this game? (Round to the nearest penny.) What is the expected payoff:
2. ### Roll a Pair of six-sided dice 5 times and getting four 4's?

What is the probability of rolling a pair of six-sided dice five times and getting four 4's? @Plato this was the other questions I am really struggling with. This is what I came up with, but I'm not sure if it is correct. p(x=4) = C(5,4) × (1/36)^4 × (35/36)^5-4 which equals...
3. ### Probability of obteining sum "S" if one roll dice "N" times

We have fair "m" sided "n" dice. What is the probability (or/and probability density function) for obtaining the sum of numbers on dice "S" after rolling them (together) "N" times. I need probability dependence on "N". "m","n" and "S" are parameters.
4. ### Roll the dice

Please help me with Player A and Player B roll a dice. They roll 5 times each. Who dices "5" first will win the game? If player A plays first, what is prob of Player A winning the game. Is it unfair?

if i roll a die 600 times. whats the mean and standard deviation of the number of 3's that show
6. ### Roll a Die question help please

if i roll a die 600 times. whats the mean and standard deviation of the number of 3's that show?
7. ### Probability of roll X or greater on Y Dice.

I want to make sure my analysis of the problem thus far is correct. I'm just learning about integer partitions so I am not sure exactly how to calculate the function I define as G(x). Assume that P(x,y) is the probality of rolling exactly X on Y Dice. This should be...
8. ### Calculating the roll and pitch of an object

Hi, I have this diagram in my notes: I can work the angles out using the cosine dot product, but then I would have an equation in arccos. I don't know how to get an equation in arctan, as has been done here. Any hints? Thanks.
9. ### Dice Roll Problem

If I were to roll 5 6 sided dice (5D6), then what is the probability of me rolling the following 5 numbers: 1,2,3,4,5 ? Basically, what is the probability of not rolling either a six or a double on 5 dice? Thank you in advance for your help! EDIT: I'd prefer the answer as a percentage rather...
10. ### Am I more likely to roll at least one six if I have more dice?

Hi, I've had a debate with some friends, about whether I'm more likely to roll at least a single 6 when I have 1000 dice, than I am to roll one with only 1 dice. I say, the more dice I have, the more likely it is to roll at least a single 6. The others try to convince me, that the...
11. ### X Attempts at a certain die roll with a retry

A friend of mine have been discussing a scenario where you get a certain amount of tries at rolling higher than a particular number on a die (for example, rolling a 3 up on a 6 sided die). Weve been trying to figure out the average amount of successes if you can retry one failed die roll. We...
12. ### Beating another player's die roll

Imagine this game: Player A rolls a number of dice, each dice has a set number of sides. For example, there might be a four-sided die with sides 1,2,3, and 4. He sums up all the numbers on his rolled dice and this number is his "power". Player B then rolls another number of dice with the same...

Roll n fair dice, and let Xn be the maximum number that is rolled. (a) [12pts] Compute E[Xn] as a function of n. (b) [4pts] What is lim(n-> inf) E[Xn]? I'm really confuse about this problem. Please help me figure out. Thanks!!!
14. ### Counting Principles, roll to dice and yield sum divisible by 3

How many ways are there to roll two distinct dice to yield a sum divisible by 3? Answer is 12. I can find the answer by writing all the possibilities down: 3 = 1+2, 2+1 6 = 1+5, 2+4, 3+3, 4+2, 5+1 9 = 3+6, 4+5, 5+4, 6+3 12 = 6+6 But how can I solve it without writing it out. Like when I...
15. ### X = # of times u need to roll to get the first 5. E(X ∣ X > 2) = (1/(1/6)) + 2 Why?

Hello, this is my first time posting here. I am studying for the P1 actuarial exam Thank you for any help :) X = # of times you need to roll to get the first 5. E(X ∣ X > 2) = (1/(1/6)) + 2 How do I get this ^ solution ^
16. ### roll of ribbon

A roll of ribbon measures 20 metres. How many 34 cm ribbons can be cut from the roll? How much ribbon will be left over? i got 0.34 x 20 m = 6.80 can be cut 13.20 m left is that correct
17. ### Ways to roll 6 dice such that there are exactly 4 unique numbers?

This one has me stumped. I've written a monte-carlo simulator, and probability of rolling such a combination is something like 50.1% My thinking is that there are C(6, 4)=15 ways to have 4 unique numbers, and for each of these there are C(6+4-1, 6)=84 ways to have 6 dice land on these...
18. ### Parabola for Golf Ball Roll on Green

Hello, I'm having a hard time coming up with a formula for showing how a golf ball will "roll" on a sloped green. For example, assume there is a right to left break of 1 degree and the ball is hit straight. The ball will end up on a path that is exactly 10 degrees to the left of the hole...
19. ### Probability of dice landing on '6' for 3rd time on the 20th roll

A die is rolled repeatedly: 1) Find the probability that the 3rd time a '6' shows is on the 20th role. 2) Generalise to the kth time on the nth roll.
20. ### Counterfeit dice roll question

A six sided die, faces numbered 1 - 6 as usual, is known to be counterfeit. The probability of rolling an even number is twice of the probability of rollong an odd number. What is the probability that, if the die is throw twice, the first roll will be a 5 and the second will be a 6? A) 2/8...