7.3 Binomial Trials • These type of experiments are called: • Binomial Trials • Bernoulli Trials • The outcomes of a binomial trial are considered as: • Success • Failure • Since there are only two outcomes, we know that: • Pr(success) + Pr(failure) = 1 • If we call: • Pr(success) = p • Pr(failure) = q • Then: • p + q = 1 and we can then say: q = 1 – p
7.3 Binomial Trials • When looking for probabilities, we use a variable to talk about what we want. • Example: • If we are tossing a coin 10 times and consider heads a “success,” then if we are looking for 3 heads, we are looking for Pr(X = 3) • 5 heads = Pr( ) • 3 heads = Pr( ) • No more than 4 heads = Pr( ) • 6 tails = Pr( ) • Because Binomial Trials have two options (p or q), there is a specific formula to calculate each situation. • Here, is the same as C(n, k) that we learned how to calculate before. • The exponents will add up to be n. • This is just like binomial expansion that we did earlier, hence the similar name!
7.3 Binomial Trials Find p and q based upon the following situations. • A coin is flipped; heads • A dice is rolled; even • A dice is rolled; one • A dice is rolled; prime • The recovery rate for a certain disease is 25% • 61% of married women are in the US labor force • 52% of students at a university are male • 76% of cars using toll booths have an easy pass
7.3 Binomial Trials A fair coin is tossed 5 times. Find the probability of achieving exactly 3 heads. The recovery rate of a certain cattle disease is 25%. If 30 cattle are afflicted with the disease, what is the probability that exactly 10 will recover?
7.3 Binomial Trials Each time at bat the probability that a baseball player gets a hit is .300. He comes up to bat four times a game. Find the probability that he gets • Exactly two hits • At least two hits
7.2 Frequency and Probability Distributions • Problems to complete from 7.3 • Pg. 354 #1 – 6
7.3 Binomial Trials Calculating Theoretical Probabilities in Binomial Trials Calculate the probabilities. Pr(X = 0) = Pr(X = 1) = Pr(X = 2) = Pr(X = 3) = Pr(X = 4) = There is going to be a four problem quiz with four options per questions. • What is the n? • What is the p? • What is the q? • What are the possibilities for k?
7.3 Binomial Trials Create a Histogram and Pie Chart for the theoretical information. Choose the correct answer. A B C D A B C D A B C D A B C D 113.76o 151.92o 75.96o 16.92o 1.44o
7.3 Binomial Trials Create a Histogram and Pie Chart for the experimental information. Analyze the results!! Are there any discrepencies? What does this say about the test-taker? What does this say about the questions? Does…