Lesson 10.1

Formula on p. 541 Suppose that in a binomial experiment with n trials the probability of success is p in each trial, and the probability of failure is q, where q = 1 – p. Then, P(exactly k successes) = n C k ∙ p k q n-k Mode: x value (number of successes) for which the probability function has its maximum value.

Example 1  The probability of getting a sum of 7 in a toss of two fair dice is known to be 1/6.  What is the probability of getting exactly 2 7s in 5 tosses. 5 C 2 ∙ (1/6) 2 (5/6) 3.16

Example 2  Suppose a baseball player has a.300 batting average.  A. If, in fact, the player has a.300 probability of getting a hit each time at bat, determine the probability distribution for the number of hits in 5 at-bats in a game

Example 2 (continued)  How unusual is it for this batter to get 3 or more hits in a game with 5 at-bats? = 16% Not particularly unusual!

Example 3  A coin that is biased so that heads occurs 60% of the time is tossed 50 times by someone who does not know it is biased. What is the probability that between 23 and 27 heads occurs, so that the person is, by mistake, rather sure the coin is fair? 50 C 23 ∙ (.60) 23 (.4) % % 254% % % 21.71%; need more tosses!

Example 4  Draw graphs of the binomial probability distributions when p =.6 when n = 10 Binomial probabilities on your calculator 2 nd vars 0 which is : binompdf(n, p, x) Where n = number of trials P = probability of success X = number of successes

 To do a binomial distribution at once…  2 nd vars 0  Binompdf (n, p)  If you would like to graph this or calculate other information, store it into a list  Ans sto L 2

n = 10, p = , ,

Homework Pages 631 –