2011-09-07, 10:34 PM
What you're talking about is known as the Binomial Probability Distribution.
The general formula for this is:
nCr p^(n-r) q^r
Where n is the number of times something is done
r is the number of successes
p is the chance of success
and q is the chance of failure
Let's take your example of rolling a 6-sided die. And you want to see if you roll 4 times, what is the probability of rolling a 3, two times.
Your n is 4, the number of times you will be rolling
Your r is 2, the number of times you want to roll a 3
Your p is (1/6), since there is a one-in-six chance of rolling a certain number on a 6-sided die, in this case, a 3
And your q is 5/6, the chance of not rolling a 3.
So now we just plug this in to the formula
4C2 (1/6)^(4-2) (5/6)^(2)
6 (1/36) (25/36)
=25/216, or a .0011% chance of success.
Hope that made sense.
The general formula for this is:
nCr p^(n-r) q^r
Where n is the number of times something is done
r is the number of successes
p is the chance of success
and q is the chance of failure
Let's take your example of rolling a 6-sided die. And you want to see if you roll 4 times, what is the probability of rolling a 3, two times.
Your n is 4, the number of times you will be rolling
Your r is 2, the number of times you want to roll a 3
Your p is (1/6), since there is a one-in-six chance of rolling a certain number on a 6-sided die, in this case, a 3
And your q is 5/6, the chance of not rolling a 3.
So now we just plug this in to the formula
4C2 (1/6)^(4-2) (5/6)^(2)
6 (1/36) (25/36)
=25/216, or a .0011% chance of success.
Hope that made sense.