Probability question with dice

Situation: When you throw 4 dice at once, the chances all the dice will be divisible by 3 is 1/16

Question: Prove the amount of dice you throw is 4.

Can somebody please explain how the amount of dice is 4?????

Here's how I tried understanding: When you throw 4 dice, there are 5 possible situations you can get all the dice divisble by 3:

1. 3,3,3,3

2. 3,3,3,6

3. 3,3,6,6

4. 3,6,6,6

5. 6,6,6,6

Then I counted all the possible situations you can get when you have 4 dice

(1,1,1,1; 1,1,1,2.....) and that adds up to 24.

So I got that when you spin 4 dice the odds are 5/24 that all the dice will be divisble by 3.

Can someone please help? Thanks

Re: Probability question with dice

For 2, you also have 3, 3, 6, 3; 3, 6, 3, 3; 6, 3, 3, 3

You have to consider each die separately.

Same for the others (Smile)

The total number of possibilities for 1 die is 6. For 2 dice, it's 6*6, and for 4 dice, you have 6*6*6*6 = 1296 possibilities

Ways to get all divisible by 3 is only when you get 3 and 6.

There are 5 'groups' of them that you got.

3, 3, 3, 3

3, 3, 3, 6; 3, 3, 6, 3; 3, 6, 3, 3; 6, 3, 3, 3

3, 3, 6, 6; 3, 6, 3, 6; 6, 3, 3, 6; 3, 6, 6, 3; 6, 3, 6, 3; 6, 6, 3, 3

3, 6, 6, 6; 6, 3, 6, 6; 6, 3, 6, 6; 6, 6, 6, 3

6, 6, 6, 6

This makes 16 in all.

The probability is then 16/1296

Hm... are you sure the dice is a regular dice? I think if it were a tetrahedron with 3, 6 and two other numbers less than 6, it'd be getting 1/16.

Re: Probability question with dice

i am sure it is a normal die. Maybe the book made a mistake.

Re: Probability question with dice

Perhaps the dice are identical and we cannot distinguish between 3363 and 3633. But, I still do not get 1/16 with this assumption!

Re: Probability question with dice

Maybe they made a mistake with the number 4. Maybe if you throw 3 or 5 dice you will get 1/16??

Re: Probability question with dice