1. Lesson Objective Understand how we can Simulate activities that have an element of chance using probabilities and random numbers Be able to use the random number generator on a calculator to simulate a practical situation

2. The Rnd# button on your calculator generates a random number between 0 and 1 every time you press it. Suppose we wanted to simulate the tossing of a coin: Read the first number after the decimal point if it is 0,1,2,3,4 = Head if it is 5,6,7,8,9 = Tail How do we simulate a fair 6 sided die? How do we simulate a biased 6 sided die where the probabilities are: P(1) = 0.1P(2) = 0.25P(3) = 0.4 P(4) = 0.05 P(5) = 0.1 P(6) = 0.1

3. Task 1 Use the Rnd# button on your calculator to decide if the Swimming pool can be completed on time using both models.

4. Task 2 Example 1 A driving instructor keeps records of passes and fails. From his records he finds the following probabilities. (i) Give a rule to use two-digit random numbers to simulate the number of attempts taken to pass the test. (ii) Use your rule to simulate the results for five learner drivers, using the random numbers below. Random numbers: 26 65 34 74 14 34 56 35 Number of attempts taken to pass the test 123456 Probability 0.20.30.20.150.10.05

5. Task 3 Example 2 A driving instructor keeps records of passes and fails. From his records he finds the following probabilities. (i) Give rules to use two-digit random numbers to simulate the number of attempts taken to pass the test. (ii) Use your rule to simulate the results for five learner drivers, using the random numbers below. Random numbers: 87 51 73 33 95 69 54 52 95 23 76 34 4 38 39 Attempt at driving test 123456 Probability of passing test 0.40.60.50.20.10.05

6. Simulating Queuing Times There are two basic approaches to model queuing situations: 1)Is to use a random number generator to calculate the times between arrivals – the arrival interval time. 2) Is to split time into chunks and then decide using a random number generator what the probability of someone arriving in that interval actually is. Eg From experiment it has been estimated that 12 people arrive at a petrol station in an hour. 0 – 2 mins probability of someone arriving is 12/30 2 – 4 mins etc

7. A petrol station wants to install a/some car washes. It always takes 12mins to wash a car in the car wash they intend to purchase. Interval between arrivals (ie. Time since last arrival) 3691215 Frequency30451555 What is the average interval time? How many car washes would you therefore recommend to meet demand?

8. 2 Car Washes 12mins to wash a car Interval between arrivals (ie. Time since last arrival) 3691215 Frequency30451555 Draw up a table to simulate the arrival of cars over a two hour period based on a 2 digit random number.

9. 2 Car Washes 12mins to wash a car Use your table to simulate the queue for the car wash if we assume they install 2 car washes and that there is a single queue with people going to the first available washer.