1. 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

2. 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!

3. 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

4. 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?

5. 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

6. 7.2 Frequency and Probability Distributions Problems to complete from 7.3 – Pg. 354 #1 – 6

7. 7.3 Binomial Trials Calculating Theoretical Probabilities in Binomial Trials 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? Calculate the probabilities. Pr(X = 0) = Pr(X = 1) = Pr(X = 2) = Pr(X = 3) = Pr(X = 4) =

8. 7.3 Binomial Trials Create a Histogram and Pie Chart for the theoretical information. XRelative Frequency Degree 00.316 10.422 20.211 30.047 40.004 Choose the correct answer. 1)A B C D 2)A B C D 3)A B C D 4)A B C D 113.76 o 151.92 o 75.96 o 16.92 o 1.44 o

9. 7.3 Binomial Trials Create a Histogram and Pie Chart for the experimental information. XRelative Frequency Degree 0 1 2 3 4 Analyze the results!! 1)Are there any discrepencies? 2)What does this say about the test-taker? 3)What does this say about the questions? 4)Does…