Simulations using the calculator or computer AP STATISTICS Simulation using the calculator or computer Using the calculator or statistical software to estimate probability through simulation is faster than doing it by hand. Problem 5.67 Tennis Racquets Professional tennis players bring multiple racquets to each match. They know that high string tension, the force with which they hit the ball and occasional “racquet abuse” are all reasons why racquets break during a match. Brian Lob’s coach tells him that he has a 15% chance of breaking a racquet in any given match. How many matches on average can Brian expect to play until he breaks the racquet and needs to use a backup? Use simulation methods to answer the question. Step 1: State the problem or describe the experiment. Brian has a 15% chance of breaking his racquet in any given match. We want to know how many matches he can play until he breaks his racquet. Step 2: State the assumptions: We can assume that the racquet use in the matches is independent. One match does not effect the other in terms of the racquet We know that he has a 15% chance of breaking the racquet leaving a 85% chance of not breaking the racquet. Step 3: Assign digits to represent outcomes: I will assign 00 to 14 to represent breaking the racquet I will assign 15-99 to represent not breaking the racquet Problem 5.67 Continued Step 4: Simulate many repetitions: Using our calculator we can generate one number at a time to decide how many matches it took Brian to break the racquet, record that number, and then repeat the simulation. RandInt(00,99,1) We will repeat the simulation twice each and then compute the average number of matches he will play before his racquet breaks. Step 5: State your conclusions: We can conclude that Brian will play an average of games before he breaks the racquet and has to use his backup. In chapter eight, we will actually Use probability models to calculate the true number of matches Brian will play before he breaks his racquet. Class Activity (5.3 Simulating Experiments) Part 2 Use your calculator to simulate a couple’s having children until they have a girl or until they have 4 children. Use the simulation to estimate the probability that they will have a girl among their children. First of all, we still have to follow the steps of simulation. Step 1: State the problem or describe the experiment: A couple will have children until they have a girl or until they have four children. Step 2: State the assumptions: We can assume that the observations are independent of each other (this means that the sex of one child will not effect the sex of the next child) A boy or girl is equally likely to occur. Step 3: Assign digits to represent outcomes: Let 0 represent a boy and 1 represent a girl. Step 4: Simulate many repetitions: Using randInt(0,1,4) we can simulate a couple’s having 4 children. We will do this 10 times each and combine our results to estimate the probability. Step 4: State your conclusions: Taking the number of desired outcomes out of the total number of repetitions, we can compute the probability of having a girl for this couple to be: Estimated probability = Now, using our calculator, we were able to do many more repetitions in a timely manor. Therefore our probability is more accurate.