If I roll three dice what is the probability that all three dice will show the same number?

Question

Help appreciated

Answer 1

you have 6/6 chance of getting a first number, since the question does not specify which one

1/6 chance of getting the same number on the second dice
and another 1/6 chance of getting the same number again on the last dice

so the answer is (6/6)*(1/6)*(1/6)=(1/36)

Answer 2

Everyone who answered that you have to multiply 1/6 * 1/6 * 1/6 and said the answer is 1/216 is missing an important point. You do not care what the first die comes up when you roll it you just care that the second and third dice come up the same as the first. So this makes the equation 6/6 * 1/6 * 1/6 = 1/36. If you specified that you wanted to roll all three dice with a specified number showing, like you wanted to roll all three ones then 1/6 * 1/6 * 1/6 would be correct.

Answer 3

Izzy is right.
Assuming you have a six sided dice, you can get any number the first time, but then your probablyity of getting the same number two times more is 1/6 each time.
The person who said 1/6 is correct for a single roll, assuming you have a six sided dice, but it isn't always 1/6, if you're rolling more than once, if you're going for a compound event, if your dice isn't 6 sided, etc.
If you wanted a specific number on the first roll that would be one in 216. 1/6 of getting it on the first roll, 1/6 on the second roll, and 1/6 on the third roll. that's why some people are saying it's one in 6^3. But look at it this way. you have 1/6^3 of getting 3 1's, 1/6^3 of getting 3 2's, 1/6^3 of getting 3 3's, 1/6^3 of getting 3 4's, 1 in 6^3 of getting 3 5's, and 1 in 6^3 of getting 3 6's. So that's 6x(1/(6^3)) = 6/(6^3) = 1/(6^2) of getting 111 or 222 or 333 or 444 or 555 or 666. (remember, with combinatorics, "or" means add and "and" means multiply)
If you have dice with some other number of sides besides 6, your chances would be 1 in n^2 where n is the number of sides, of getting the same number 3 times, and 1 in n^(m-1) of getting the same number m times.

Answer 4

I don't usually answer questions where there are right answers, but there are so many *wrong* ones here too.

The answer is 1/36. The chance of getting 3 1's is 1/216, the chance of getting 3 2's is 1/216... the chance of getting 3 6's is 1/216, the chance of getting 3 of anything is 6*1/216 = 1/36.

First die can be anything, second has a 1/6 chance of matching, third has a 1/6 chance of matching. 1/36 - *not* 1/216.

Answer 5

You are still going to have to times 1/6 * 1/6 * 1/6 even though it doesnt matter which dice you are wanting. You still need to have all three the same the probability will need to be taken into consideration for each. The answer would 1/216.

Answer 6

K

SO, there are 3 dies with 6 possible results on each one.

So, lets pretend the number is 1.

First roll: 1/6 chance
Second roll: 1/6 times the 1/6 of the first chance, which is 1/36
Third roll: 1/6 times the second roll: 1/216

Result = 1/216
0.00462...%

Answer 7

With dice, your chances of anything will always be 1/6.

Answer 8

yes, all those that answered 1 chance in 216 are correct
1/6 ^3 = 1 in 216

Answer 9

A 50-50 chance

Answer 10

it would be 6x6x6 which is also 6 to the 3rd.

so its 216