1. Binomial Trials: Success/Failure 2. Probability of k Successes 1

2 An experiment with just 2 outcomes is called a binomial trial (or Bernoulli trial. ) One outcome is labeled a success and the other is labeled a failure. If p is the probability of success, the q = 1 - p is the probability of failure.

 Examples of binomial trials:  1. Toss a coin and observe the outcome, heads or tails.  2. Administer a drug to a sick individual and classify the reaction as "effective" or "ineffective."  3. Manufacture a light bulb and classify it as "nondefective" or "defective." 3

4 If X is the number of "successes" in n independent trials, where in each trial the probability of a "success" is p, then for k = 0, 1, 2,…, n and q = 1 - p.

5 Each time at bat the probability that a baseball player gets a hit is.300. He comes up to bat four times in a game. Assume that his times at bat are independent trials. Find the probability that he gets (a) exactly 2 hits and (b) at least 2 hits.

6 Each at-bat is considered an independent binomial trial. A "success" is a hit. So p =.300, q =.700 and n = 4. X is the number of hits in four at-bats. (a)(a)

7 (b) "At least two hits" means X > 2.

 If the probability of success in each trial of a binomial experiment is p, then the probability of k successes in n trials is where q = 1 – p. 8