Are these odds right?

Factual Questions
1

No, this is not my homework.

Two six-sided dice are rolled (they have the standard values).

The number of the first dice is multiplied by the number of the second. So if a 2 and a 5 are rolled, the result is 10.

Possible results:
1,2,3,5,6,8,9,10,1215,16,18,20,24,25,30,36

If a number has already been rolled, then the next “unrolled” number is used. The numbers 1, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30 have already been rolled.

The way I see it the chances of the remaining numbers look like this. We are 3 people who rekon this looks right, but I thought that who knows better than the dopers :slight_smile: I am still in pain from trying to follow the discussion of the NY lottery results that time.

36 = 56%
5 = 14%
6 = 11%
2 = 7%
3 = 7%
8 = 6%

That look right to you guys?

2

Just a quick note. The possible results should be
1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36

3

It looks off to me, but I think I’m misunderstanding the problem. What do you mean, the next unrolled number? The next highest unrolled number?

4

Sorry that is correct, and 4 is gone already (which is why 5 has a higher chance, since 5 will be the result even if 2x2 is rolled).

5

Okay, why doesn’t 2 have a higher probability than 3? There are three ways to get 2 (1x1, 1x2, 2x1) but only two ways to get 3 (1x3, 3x1).

6

This is where I complicate the issue by saying that 2 and 3 are the same number in that they give the same result… Lets say that 36 gives me a snickers, 8 gives me a …hmm… an icecream and both 2 and 3 result in a pack of m&m’s …

Does that make sense? Two and three are the only ones of the results “still open” that have the same value.

7

The odds are

2 - 8.33%
3 - 5.56%
5 - 13.89%
6 - 11.11%
8 - 5.56%
36 - 55.56%

8

So let me get this straight. There’s a 14% chance of getting either 2 or 3. So even though 2 is more likely than 3, you split up the chances evenly? I don’t think that’s the best way to do it, but if that’s the way you’re doing it, I’d say your math is right.

9

Sorry Achernar, I had it worked out as 2or3 = 14% but I thought that would be confusing, so I split them in half! :smack: seems I confused things even more. Seems like we were in the ballpark on the numbers tho :slight_smile: thats pleasant!

10

I come up with



2  :  3/36
3  :  2/36
4  :  3/36
5  :  2/36
6  :  4/36
8  :  2/36
36:  21/36