SA Footy

A question: What is the likelihood of rolling one dice two times and getting a number 4 and a number 5?

I think it's 2 in 36...

either the 4 or 5 in the first roll could be paired with the 5 or 4 from the second roll, 36 possibilities.


but could it be 4 in 12? 6 possibilities first roll, 6 second roll.

I'm sure it's obvious why the (second?) idea is wrong... can anyone explain to me why?

2 out of 36, or 1 in 18 it would be.

I would say the second one would be wrong because you are counting two rolls of the dice as one set.

Excellent, much appreciated. Cheers, Spelly!

Wouldn't it be 2 in 6 (rolling a 4 or 5) multiplied by 1 in 6 (either the 4 or 5 depending in which you hit the first time)?

With that 2nd option, that would be a hypothetical on the chances of rolling a 4 or a 5 in two rolls of the die. You would be counting each roll seperately.

Constance_Perm wrote:Wouldn't it be 2 in 6 (rolling a 4 or 5) multiplied by 1 in 6 (either the 4 or 5 depending in which you hit the first time)?

Well, I guess the best way to definitely be sure is to list the possibilities of the first scenario:

1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6

There's only two out of the 36 possible outcomes to match the criteria.

Sploosh wrote:but could it be 4 in 12? 6 possibilities first roll, 6 second roll.

I'm sure it's obvious why the (second?) idea is wrong... can anyone explain to me why?

Because when you are counting one set of possibilities combined with another it multiplies rather than adds.

Constance_Perm wrote:Wouldn't it be 2 in 6 (rolling a 4 or 5) multiplied by 1 in 6 (either the 4 or 5 depending in which you hit the first time)?

Agreed - assuming that the first time a 4 OR a 5 was an option.

If it was a 4 first and a 5 second (or vice versa), it would be 1/6 x 1/6. (This also assumes it is a 6-sided dice numbered 1,2,3,4,5,6!).

Sploosh wrote:A question: What is the likelihood of rolling one dice two times and getting a number 4 and a number 5?

I think it's 2 in 36...

either the 4 or 5 in the first roll could be paired with the 5 or 4 from the second roll, 36 possibilities.


but could it be 4 in 12? 6 possibilities first roll, 6 second roll.

I'm sure it's obvious why the (second?) idea is wrong... can anyone explain to me why?

With the first roll odds are 2 out of 6 ( either 4 or 5) 2/6 = 1/3
2nd roll ( based on making first roll ) odds are 1/6

therefore odds are 2/6 x 1/6 = 2/36 =1/18

That's correct OWW

Thanks all. I feel goodly learnerated.

Sploosh wrote:Thanks all. I feel goodly learnerated.

back to kiling whales now...?

Punk Rooster wrote:back to kiling whales now...?

Serve 'em up with a nice salad and the meat is quite tasty, thank you very much!