is this the correct way to solve this question? when two fair dice are rolled,the odds of throwing a 'double'(two dice with the same number) is 1:5.
if two dice are rolled 400 times ,the best estimate of the number of times you would NOT get a double would be ___? 
my work:
400/2=80/2=40
is this the correct answer to the solution and if not ,what is the correct answer to this question?
 A: Start by calculating the probability of getting a double of a particular number (1 for instance).
Each dice has 6 numbers, so the probably of getting 1 on a single dice is $\left(\frac 16\right)$.  The probability of getting 1 on both dice is the product of the probabilities of getting 1 on each individual dice: $$\left(\frac 16\right)\left(\frac 16\right)=\left(\frac{1}{36}\right)$$
Now, multiply that result by 6 to calculate the probability of getting a double of any of the 6 numbers.
$$\left(\frac{1}{36}\right)6=\left(\frac{1}{6}\right)$$
The probability of rolling a double is $\frac 16$.
To calculate the theoretical amount of rolls (out of 400) that will not be doubles, take 1 minus the probability of rolling a double, and then multiple that result by 400.
$$\left(1-\frac{1}{6}\right)400=\left(\frac{5}{6}\right)400=333$$ (I rounded to the nearest whole number)
A: So lets try to calculate the number of times we would throw a 'double', given the probability is 1:5 , and n=400.
So if we were to throw the pair of two dice once, there is 1/5 chance that they would be a double. If we were to throw it again, the probability will still stay the same; so no matter how many times you throw the dice, the probability will always be 1/5.
The probability of 1/5 means that if we were to throw our pair of dice 5 times, atleast 1 of those times the dice will be a 'double', because we multiply the number of times we rolled our dice, 5, by the probability. So we end up $5*\frac{1}{5}=1$, the number of times a double occurred if we threw the dice 5 times. To calculate the number of times a 'double' was thrown we use the same logic, we multiply the number of times we threw the dice by the probability: $400*\frac{1}{5}=80$, so out of the 400 dice rolls, only 80, will be double. 
To calculate the number of rolls that were not a double, we minus the total number of rolls by the number of rolls where a double occured: $400-80=320$. So out of the 400 dice rolls, 320 of them will not be a double. 
