# Ch 5.3

 The flashcards below were created by user khonka on FreezingBlue Flashcards. Factorals 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 independet3. 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 Assumptions1. n trials are to be performed2. Two outcomes, success or failure, are possible for each trial3. The trials are independent4 The success probability, p, remains the same from trial to trialStep 1. Identify a success,Step 2. Determine p, the success probabilityStep 3. Determine n, the number of trialsStep. 4 The binomial probability formula for the number of successes, X, is given by P(X=x) = (n/x) px(1-p)n-x or nCx px qn-x wher q=1-p Cumulative probability < uses less then or equalP(X