# Dice probability

new_at_math
Say you roll a dice twice.You want to calculate the probablity of getting both dice to land on 3. Using the formula for combinations: the total number of combinations is 21. so is the probabilty of getting a 3 on both dice 1 /21 ?

The probability of rolling a three on a six sided die is ##\frac16##. Doing it twice is ##\frac{1}{6} \cdot \frac{1}{6} = \frac{1}{36}##

new_at_math
explain

I don't see the logic
how is it permuation formula(combination formula ).
What is wrong with my method?

economicsnerd
Whatever formula you have in mind, but there are 36 possible outcomes: $\{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}$
If each of these seems equally likely to you, then the answer is $\frac1{36}$.

• 1 person
economicsnerd
I'm guessing your method was to plug in "6 choose 2", which is the formula that tells you how many ways to pick a pair of people from a collection of 6 people. That doesn't describe the situation you named.

Homework Helper
hi new_at_math! Say you roll a dice twice.You want to calculate the probablity of getting both dice to land on 3. Using the formula for combinations: the total number of combinations is 21.

no, you're completely misunderstanding what combinations are for 21 is the number of different results you can get from two seven-sided dice if you're not allowed doubles …

12 13 14 15 16 17 23 24 25 26 27 34 35 36 37 45 46 47 56 57 67 …

start again: write out the possible combinations for a 3 (you did mean 3-total?) new_at_math
I get it now it was a permutation with repetition;my bad.

economicsnerd
Say you roll a dice twice.You want to calculate the probablity of getting both dice to land on 3.
I don't believe any formula with the word "permutation" or the word "combination" is an effective way to approach this problem.

I get it now it was a permutation with repetition;my bad.

No. Permutation is a rearrangement of a collection of objects.
Your example is a Bernoulli trial.