Binomial Distribution

binomial distribution

a discrete probability distribution that addresses experiments or processes (ex: trials) that can result in one of 2 mutually exclusive outcomes

what are the criteria that must be met for the procedure of a binomial probability distribution

1) the number of trials are fixed and independent

2) each trial results in one or two possible, mutually exclusive outcomes:

• “success” - the outcome we are interested in

• “failure” - the secondary outcome

3) the probability of a “success” and the probability of a “failure” remain constant from trial to trial

what is a success defined as

the outcome we are interested in

what is a failure defined as

the secondary outcome

if the assumptions hold true what can be used

the binomial probability formula

what does the binomial probability formula calculate

the probability of obtain exactly X “successes” among n trials

what is this formula

binomial probability formula

what does n represent in the binomial probability formula

number of trials

what does x represent in the binomial probability formula

number of successes among n trials

what does p represent in the binomial probability formula

probability of “success” on any given trial

what does q represent in the binomial probability formula

probability of a “failure” on any given trial

factorial

the product of decreasing factors

how is a factorial represented

!

what would 4! be

24

• 4×4×2×1