Starter   In a certain game show, a contestant is presented with three doors. Behind one of the doors is an expensive prize; behind the others are goats. The contestant is asked to choose a door. The game show host, Monty, then opens one of the other doors to reveal a goat behind it. The contestant is then asked if she/he would like to stick with the original door or switch to the remaining door. Why is it better to switch doors each time? Explain. Firstly run a simulation using the site below. Play the game 20 times, switching each time. The computer simulation will keep track of the experimental probability. http://www.shodor.org/interactivate/activities/SimpleMontyHall/ Write down the experimental probability of winning when you switch doors each time. Probability of winning is ___________________

Activity 1:   Your friend says that when he tosses a fair coin 2 times the probability that he gets exactly 2 heads is one quarter. Explain what he means. Can you come up with a simulation on your calculator that will show that his suggestion is probably correct?

  Activity 2: When throwing four fair coins at the same time, what are your chances of getting exactly two heads? Simulate this with you calculator randInt (1, 2, 4) In this case 1 represents a head and 2 represents a tail. With your partner run this 50 times recording the number of times you get two heads. Record your results on the whiteboard. Your experimental probability of getting two heads was _______________________ The class’s experimental probability of getting two heads was _____________________ Why are the class results probably more accurate? Draw a tree diagram to find theoretical probability

Activity 3:   With your partner and using your calculator, simulate throwing two fair 6-sided die and adding the total on top. This can be done by randInt (1,6,1) + randInt (1,6,1) = Do this 100 times and record the number of 7’s. Add your results to the teacher’s table on the white board. Your experimental probability of getting a sum of 7 was _______________________ The class’s experimental probability of getting a sum of 7 was _____________________ Draw a diagram to find theoretical probability

Activity 4: Chevalier de Mere was a mid-seventeenth century high-living nobleman and gambler who attempted to make money gambling with dice. Probability theory had not been developed, but de Mere made money by betting that he could roll at least one 6 on four rolls of one die. Experience led him to believe that he would win more times than he would lose with this bet. Was he right? Create a simulation with 20 trials and count the number of times you win. Record your results in the teacher’s table on the white board. What appears to be the probability of winning this game?

Activity 5: The Duck Hunters There are 10 fraternity brothers at a shooting gallery at the State Fair. Each brother is a perfect shot, meaning that they never miss the target they are aiming at. Ten cardboard ducks appear simultaneously, and each shooter picks one of the ten ducks at random, takes one shot, and hits his target. Design and carry out a simulation to estimate the average number of ducks.

Homework: 22A: 1, 4 22B: 1,2 22C.1: 3, 5, 7 22C.2: 2, 3 22D: 1, 3