Using Technology to Conduct a Simulation 6.4 Using Technology to Conduct a Simulation How can you use technology simulations to estimate probabilities?

Texas Essential Knowledge and Skills The student is expected to: Proportionality—7.6.B Select and use different simulations to represent simple and compound events with and without technology. Mathematical Processes 7.1.C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

ADDITIONAL EXAMPLE 1 The probability of spinning the winning letter in a game show is 20%. What is the experimental probability that a contestant will spin exactly four times before spinning the winning letter? Check students’ work. Note that the winning letter can be represented by 2 numbers out of 10 or 1 out of 5 and each trial will end when the designated number that identifies the winning number is generated.

ADDITIONAL EXAMPLE 2 There is a 25% chance that a canal will flood during any given year. What is the experimental probability that the canal will flood in at least 1 of the next 6 years? Check students’ work. Note that a flood should be represented by 1 out of 4 possible numbers in the simulation, and each trial should contain 6 random numbers generated from 1 to 4.

6.4 LESSON QUIZ 7.6.B At a restaurant, 60% of customers typically order a salad with their meal. What is the experimental probability that the next 4 customers will order a salad? 1. Describe a model to simulate the event. Sample model: 60% = ; Let 1, 2, and 3 represent customers who order a salad. Let 4 and 5 represent customers who do not order a salad. For each trial, generate 4 random numbers. Count the number of trials where all four numbers are 1, 2, or 3.

At a restaurant, 60% of customers typically order a salad with their meal. What is the experimental probability that the next 4 customers will order a salad? 2. Use a simulation to find the probability. Check students’ work.

There is a 10% chance that a box of tiles in a shipment will contain broken tiles. What is the experimental probability that there will be broken tiles in a box in at least 1 of the next 5 shipments? 3. Describe a model to simulate the event. Sample model: 10% = ; Let 1 represent a box with broken tiles. Let 2–10 represent a box with unbroken tiles. For each trial, generate 5 random numbers. Count the number of trials that contain at least one 1. 4. Use a simulation to find the probability. Check students’ work.

Recall from Your Turn Exercise 1 that an elephant has a 50% chance of giving birth to a male or female calf. Use a simulation to determine the number of male calves in three births. Use the results of your simulation to complete the table. Check students’ work.

How many trials did you perform in your experiment? Why? Answers may vary. What do you notice about the frequencies of the different numbers of male births? Answers may vary. In most simulations, there will be a noticeably larger number of outcomes with 1 or 2 males than with 0 or 3 males.

How can you use technology simulations to estimate probabilities? Sample answer: Use a calculator or computer to generate random numbers to simulate an experiment. Use the results to estimate probabilities.