Two dice are rolled, Find the odds in favor of:?

Question

a) the sum of the numbers being a 12.
b) one of the numbers is a 3 and the other is a 6
Book answer:
a = 1:35
b = 1:17

--- I keep getting 1/36 for both. Are the answers in the book wrong?

Answer 1

a) Try counting the possibilities.
There is only one way to roll a 12...(6, 6)
and there are 36 different possible rolls.
so the chances are 1/36

b) There are 2 possibilities for this one (3, 6) and (6, 3)
so it's 2/36 or 1/18

The difference between the book the you is notation.
1:35 means that for every one success there are 35 failures.
1/36 means that there is one success for every 36 tries.

Answer 2

Odds are the favorable outcomes/ unfavorable outcomes
For a:
I think the book is right because my answer tallies here. So, first I listed them:
Die 1:1,2,3,4,5,6
Die 2:1,2,3,4,5,6
Number of ways to get the addition of twelve: 1. Only 6+6 equals 12. Thus, the number favorable is 1.
Now the other options are not favorable. The number of combinations that are unfavorable outcomes are 35 since the total outcome (36) minus the favorable outcome (1) is 35.
Thus, the answer is 1:35
As for b:
I think the book is right. The answer is 1:17 because the first we have to take notice of the "and". That means that we have to multiply. So, I would multiply 3 and 6. Then that gives the total number of possibilities. So, subtract only 1 (because 3 in die 1 and 6 in die 2 can occur in only 1 way-- it's NOT the same as 6 in die 1 and 3 in die 2) from 18. Then, you get 17. So, since there is only 1 way 3 can be die 1 and 6 can be die 2, the favorable outcome is 1 over the unfavorable is 17.
But if u want the PROBABILITY of favorable outcomes, it's different. But, you asked for odds, so basically, I think the answers are:
1: 35 and 1:17. I hope I got them right and that I helped.

Answer 3

Checked your profile. You're just posting your homework problems. You'll never learn that way!

But this one, okay, you're questioning the answers in the book, and I think that's fair. For part a, there are 36 possible rolls. There is only 1 way to get a total of 12 (both sixes). I agree, right answer is 1:36.

As for part b, I actually think it's 1:18. Think of one of your dice as die #1 and the other as die #2. There are 2 ways (out of the 36 possible rolls) to get a 3 and a 6. Either die #1 has the 3 and die #2 has the 6, or the other way around.

Answer 4

There are different ways of expressing the same probability.

35:1 reads as "35 to 1", meaning 35 chances against, and 1 chance for.
1/36 is "one in 36", meaning 36 chances total, and 1 chance for.

For the second problem, you're counting the chances wrong.
You have 2 chances, either you roll a 3-6 or a 6-3.
So it's 34:2, or 2/36, which reduces to 17:1 or 1/18.

Answer 5

Book is right. To get 12 you can only have a 6 on each die. To get 3 you can have a 1 on die A and a 2 on die B or a 2 on Die A and a 1 on die B. Therefore, two ways to make a 3 and only one way to make a 12.

Answer 6

The probability for getting a sum 12 will be 1/36 (6,6)
The probability for one of the die to be a 3 and the other to be a 6 will be 1/18 [(3,6),(6,3)]

Answer 7

2 specific numbers = 1/36

since 6 + 6 are the only 2 numbers that add up to be 12

In otherwords are need to roll doubles

a.) 1/36

Here is how to get it. (1/6) of rolling a 6, probability of rolling 2 6s, is (1/6)(1/6) = (1/36)

---------------------------------

b.)
3,6 or 6,3
the answer should be either (1/18) or (1/9)

Answer 8

odds for a 12 is 1/18? Thanks! that'll help my craps play. errr craps game.