1. Randomness, Probability, and Simulation
Grab your computer

2. http://digitalfirst.bfwpub.com/stats_applet/stats_ap plet_10_prob.html

3. Tossing a Coin
If you toss the coin just once, what are the possible values for the proportion of heads?
If you toss the coin 400 times with probability of 0.5 for heads, which is more likely to happen: (a) getting exactly 200 heads or (b) getting within a few percent of 200 heads?
What will the plot of the proportion of heads look like as you accumulate more and more tosses with a probability of 0.7 for heads?
(test out your answers via the applet)

4. Tossing a Coin (cont)
Set the probability of heads at 0.3 and have the applet repeatedly toss the coin until you accumulate several hundred tosses. How does the behavior of the proportion of heads at the beginning of the plot differ from that at the end of the plot
Check the “Show true probability” box to have the applet draw a horizontal line on the plot at 0.3. How does the behavior of the plot of the proportion of heads relate to this line?
Change the probability of heads to 0.7 and have the applet toss the coin several hundred times again. How does the plot of the proportion of heads compare with the plot when the probability was 0.3? In what ways is it similar? Different?

5. Probability: Long Run
Toss a coin many times. The proportion of heads changes as we make more tosses but eventually gets close to 0.5.
“The probability of a tails is ½”

6. Thumbtacks Do thumbtacks behave the same as coins?
What is the probability that the tossed thumbtack will land point up?

7. Thumbtacks
What do you predict will happen? What proportion of thumbtacks will land point up?
Toss your thumbtack 50 times. Tally the # of point up and point down landing. Calculate proportion of point up.
What would you estimate as the probability of your thumbtack landing point up if you tossed it one more time?
Combine your data with 5 classmates

8. Thumbtacks
5. What proportion of thumbtacks will land point up? 6. Do thumbtacks and coins have the same probability? 7. What do you think the graph of the thumbtacks would look like? Modify the applet to be the proportion in #5 and draw the graph.
They have the same number of ‘sides’

9. Vocab Random Probability
Random: does not mean haphazard, a phenomenon is random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions
Probability: a number between 0 and 1 that describes the proportion of times the outcome would occur in a long series of repetitions

10. Match This event is impossible. It can never occur 0.01
This event is certain. It will occur on every trial.
This event is very unlikely, but will occur once in a while in a long sequence of trials
This event will occur more often than not.
0.01
0.3
0.6
0.99 1

11. How many tosses to get a tail?
When we toss a penny, experience shows that the probability of getting tails is close to ½. Suppose we toss a penny until we get tails. We want to know the probability that the first tail comes up in an odd # of tosses.
Perform 30 trials and keep a record of the # of tosses needed to get tails
Estimate the probability of getting tails on the first toss.
Combine your results with 4 other classmates to estimate the probability that the first tail appears on an odd- numbered toss.