Trial - each reptition, particularly the experiment (each trial) has only two possible outcomes. ex. testing the effectiveness of a drug: for each patient the drug is either effective or not effective ( 2 possible outcomes)
k! = k(k-1)..2x1...
0! = 1
Binomial Coefficients
if n is a positive integer and x is a nonnegative integer less than or equal to n, then the binomial coefficient (n )is defined as
Bernoulli Trials
are repeated trials of an experiment, if the following 3 conditions are statisfied:
1. the experiment (each trial) has two possible outcomes, denoted generically s, for success, and f, for failure
2. the trials are independet
3. The probability of a success, called the success probability and denoted p, remains the same from trial to trial
Binomial distribution
is the probability distribution for the number of successes in a sequence of Bernoulli trials
To find a Binomial Probability Formula
Assumptions
1. n trials are to be performed
2. Two outcomes, success or failure, are possible for each trial
3. The trials are independent
4 The success probability, p, remains the same from trial to trial
Step 1. Identify a success,
Step 2. Determine p, the success probability
Step 3. Determine n, the number of trials
Step. 4 The binomial probability formula for the number of successes, X, is given by