MBF 3CI2-3 Comparing Experimental &Theoretical Probability
Simulation –
Expected Value –
Expected Value =
Simulating with a Spinner
Given the spinner below, what is the theoretical probability of the spinner landing on red?
PT(red) =
How many times should we get red if we spin four times?
Will this always happen?
Spin four times. What is the experimental probability of red?
PE(red) =
Spin 8 more times. What is the new experimental probability of red?
PE(red) =
What happens to the experimental probability as we increase the number of trials?
Trial / Number of Heads / Average Number of Heads1
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Simulating with a Coin
If you toss a coin 10 times, how many times do you expect to turn up heads? Explain your reasoning.
Toss a coin 10 times. Record the number of times that heads turns up. The 10 tosses represent one trial. Record the average number of heads.
Repeat the experiment. Record the number of times that heads turns up in the second column.
Average Number of Heads = Total Number of Heads ÷Trial Number
Repeat until you have completed 10 trials.
Draw a scatter plot of the Trial Number vs Average Number of Heads.
Reflect:
What do you notice about the graph as the number of trials increases?
Why do you suppose this is the case?
Do you think this is always the case? Explain.
Simulating with a Graphing Calculator
Trial / Number of Girls1
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What keys do you need to press to get into the probability function?
How do you generate three random integers between 1 and 6?
What command would you use to simulate the gender of three children?
What is the theoretical probability a family with three children has two girls?
If 25 different families each had three children, how many families would you expect to have two girls?
Use the graphing calculator to simulate 25 trials.
What is your experimental probability of two girls?
What was the experimental probability for the class?
Creating a simulation
On a recent test, Dante scored 13.5 out of 30.
a) Suppose any question is selected at random. What is the probability that Dante got that question correct?
b) Describe how to make a spinner to simulate Dante getting a random question correct.
c) On a graphing calculator, press Math, select PRB and then 1:rand. Press Enter several times. Record three of these results.
d)How could this method be used to predict whether or not Dante got the question correct?