Dice Roll Probability Questions...?

Question

You roll 3 regular dice. Before each roll, you pick a number from 1-6. If you roll all three dice and your number comes up once, you get 2 points. If it comes up on two dice, you get 4 points. If all three dice come up with your number, you get six points. If your number does not come up on a single roll, you get 0 points.

1) How many combinations are possible on a single roll of all three dice?
2) What are the odds of your number coming up at least once on a single roll of the three dice?
3) How many points will you have if you roll each possible combination once?

First person to correctly answer all 3 questions will have my undying admiration and 10 points for best answer!

P.S. - Guessing will not get the right answers, You must actually figure it out.

Got a right answer already! 10 points goes to Nielman for being the first with the right answer to all 3 questions. Thanks, everyone! I'll be back with another, more challenging question soon.

Nielman, I have to wait 24 hours to post your best answer, but I won't forget.

Answer 1

number one is 216 different combinations.
number two is 1-125/216 or 91/216 that is 1 being the certainty minus (5/6)^3 5/6 is the probability of your number not coming up on any dice to the third power for having three dice
number three is harder: hmmmm
1/6*5/6*5/6*3 for one number or 75/216 for one number for 150 points
1/6*1/6*5/6*3 or15/216 for two numbers coming up for a total of 60 points.
one possible combination eg you pick a four and three fours come up is worth six points so the total number of points is that number 216. Which makes the expected value of a random roll of the dice equal to one.

That was fun and thank you

Answer 2

The three 6 sided dice present 216 different combinations.

You will pick one number. You have 18 dice sides, and one number which will appear three times. The chances of your number coming up are therefore 3/18, which can be simplified to 1/6. Every 6 rolls, your one number should come up.

I assume we will remain with one number. I will pick one. Out of all the combinations, 1 appears once in 25 occasions. That would grant 50 points. The number of instances that one appears twice is 10. That would give you 40 more points. One appears three times only once, so that's 6 points. 50+40+6 is 96 points. You'd only get 96 points.

Answer 3

1. Possible combinations: 6x6x6=216
2. 1/6 + 1/6 + 1/6 = 1/2
3. 6 pts = all 3 dice = 1 combination possible = 6 pts
4 pts = 2 of 3 dice = 5 + 5 + 5 = 15 combinations = 60 pts
2 pts = 1 of 3 dice = 25 + 25 +25 = 75 combinations = 150 pts
Total = 216 points

Answer 4

1) The dice roll results are independent of each other, so the no. of combos ....
6^3= 216
2) Now, we have that one dice must have a 3 (here I choose 3 as my number), the rest can be any
So we have.....
6^2*3=108 combos with a 3
So my chance for 1 '3', is 108/216*100=50%
3) I get 2 points for each combo with 3
No of combos with one 3: One dice is 3, second can be any other then 3, same for third.......5^2=25 .So points, 25*2=50
No of combos with two 3s: Two dice are three, rest is any
except 3..... 1^2*5=5 Total points: 5*4=20
No of combos with all threes:obviously one. Points:1*6=6

So my total points are......50+20+6=76 POINTS

Answer 5

6*6*6 = 216 possible combinations, 1/6 /3= 50 percent chance of getting one num right in 3 dice, 54 points total for each combo once. 6 pointer once, 4 pointer 3 times, 2 pointer 18 times

i just took a genetics final so if i didnt get at least two right for your question i am in big trouble on the final.....:)

Answer 6

18

Answer 7

1) 216 combinations
2) 2 to 1 (50%)
3) 24 points

Answer 8

1. 216 combos (6x6x6)
2. 1/6 + 5/36 + 25/216 = 91/216 you will get at least once
3. 216 points (36 times each die will roll your number)

Answer 9

I can tell you this keep the dice tight in your hand and the numbers you want to come up on the bottom and they will the majority of the time.

Answer 10

1. 1/6 * 1/6 * 1/6 = Answer: 1/216

2. 3/216

4. 12