Binommial Distribution FormulaP(x) = (n! / (n - x)!x!)pxqn-x
n: The number of trials
x: The number of successes
p: The probability of success
q: The probability of failure (which is 1 - p)
The binomial distribution describes the behavior of a count of variable X if the following conditions apply:
- 1- The number of observations n is fixed.
- 2- Each observation is independent.
- 3- Each observation represents one of two outcomes ("success" or "failure").
- 4- The probability of "success" p is the same for each outcome.
Sample Binomial Distribution ProblemAlex has a nickel and he is going to flip it 3 times, what is the probability of the coin flips resulting in 2 heads?
Below is the possible results:
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
To solve for this problem using the formula, it will look like the following:
n: 3 (3 flips)
x: 2 (there are only two alternatives, heads or tails)
p: .5 (there is a 50% probability of getting heads)
q: .5 (there is a 50% probability of getting tails)
P(2 heads) =
(3! / (3 - 2)!2!).52.53-2
The answer to this problem is .375, which means there is a 37.5% probability of 2 heads occuring out of 3 flips.