5.3 Simulating Experiments

5.3 – Simulating Experiments Classwork

1. Use your calculator to simulate a couple’s having children until they have a girl, or until they have four children, whichever comes first. Use the simulation to estimate the probability that they will have a girl among their children.

2. Suppose that in a particular year, the American League baseball team is considered to have a 60% chance of beating the National League team in any given World Series game. To win the World Series, a team must win 4 out of 7 games in the series. Further assume that the outcome of each game is not influenced by the outcome of any other game (that is, who wins one game is independent of any other game). Use simulation methods to approximate the number of games that would be played in order to determine the world champion.

3. 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. If a player has a 15% chance of breaking a racquet in any given match, how many matches (on average) can he expect to play until he breaks a racquet? Use simulation to answer the question.

4. Amarillo Slim is a card shark who likes to play the following game. Draw 2 cards from the deck of 52 cards. If at least on of the cards is a heart, then you win $1. If neither is a heart, then you lose $1. - Describe the correspondence between random numbers and possible outcomes in this game (that is, identify what the possible outcomes are and assign random numbers to them) - Simulate playing the game for 25 rounds. You can assume that you shuffle the cards after each round. Can you beat Amarillo Slim at his own game? Write down the results of each game – combine your results with other students to get a total of 100 trials. Report your cumulative proportion of wins. Do you think this is a “fair” game? Do both you and Slim have an equal chance of winning?

5. Another game of change is based on randomly selecting three numbers from 00 to 99 inclusive (allowing repetitions) and adding the numbers. A person winds the game if the resulting sum is a multiple of 5. - Describe your scheme for assigning random numbers to outcomes in this game - Use simulation to estimate the proportions of times a person wins the game

6. Happy Birthday! Use your calculator and the simulation method to show that in a class of 23 unrelated students, the chances of at least 2 students sharing a birthday are about 50%. Then show that in a room of 41 people, the chances of at least 2 people having the same birthday are about 90%. What assumptions are you using in your simulations?