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Suppose we roll 10 fair six-sided dice. What is the probability that there are exactly two 2’s showing? Solution: There are ${10\choose2} = 45$ ways of choosing which two dice will have 2 showing. Then the probability that those two dice show 2, and the other eight do not, is $(1/6)^{2}(5/6)^{8}$. So, the answer is $45(1/6)^2(5/6)^8 = 0.2907$
Here's another example. If you throw a 6-sided dice 10 times, there is 1/4 probability that the sum is a multiple of 4. The program above should run with the following parameters: int t_throws = 10; int s_sides = 6; int x_multiple = 4;
When trying to find how to simulate rolling a variable amount of dice with a variable but unique number of sides, I read that the mean is $\dfrac{sides+1}{2}$, and that the standard deviation is $\sqrt{\dfrac{quantity\times(sides^2-1)}{12}}$.
If I roll a 10-sided dice and I get 6 or more as a result, I get a "success". But if I roll the dice and I get 1, it cancels one success, so that If I roll two times the dice and I get (7,1), I have 0 success, if I roll it and I get (7,2), I have one success, if I roll it and I get (1,1) I have -2 success.
Further, the chance that the first roll is greater than the second must be equal to the chance that the second roll is greater than the first (e.g. switch the two dice!), so both chances must be $2.5$ out of $6$ or $5$ out of $12$.
Assuming a fair six sided dice . The probability of rolling a 4 or more (4, 5 or 6) from a single roll is $\frac{3}{6} = \frac{1}{2}$ as there a three winning results and 6 possibilities. The probability of rolling a 5 or more (5 or 6) from a single roll is $\frac{2}{6} = \frac{1}{3}$ as there a two winning results and 6 possibilities.
You continually roll a fair $10$ sided dice. What is the expected number of rolls until the lowest common multiple of all numbers that have appeared is greater than $2000$? The primes in the numbers $1$ to $10$ are $2,3,5,7$. The lowest common multiple of these numbers is $210$.
With two dice, you can get a six or greater if the first dice is six or greater (50%) or the first dice is less than 6 (50%) but the second is greater than six (50%). So, the total in this scenario, since the two dice rolls are independent is 50% + 50%*50% = 75%.
A fair 6-sided die is rolled 10 times and the resulting sequence of 10 numbers is recorded ...
There is a $20$-sided (face value of $1$-$20$) die and a $10$-sided (face value of $1$-$10$) dice. $A$ and $B$ roll the $20$ and $10$-sided dice, respectively. Both ...