Coin Tossing
You can use this manipulative to explore many different chance processes.
Enter the number of times you want to toss the coin. Click Start . You can view the entire run of coin tosses by moving the slider.
Select Longest run of heads and enter the number of heads in a row that you wish to occur. Click Start for the coin to be tossed until your desired run is achieved.
Chance Error
With any number of tosses there is a chance error in the number of heads that occurs. If the coin is fair (probability of heads = 0.5), then the chance error is equal to the difference between the number of heads and half the number of tosses. For example, if you toss a fair coin 100 times and observe 54 heads, then the chance error is 4. If you observe 43 heads in 100 tosses of a fair coin, then the chance error is -7.
The chance error is likely to get larger as the number of tosses increases. Set the probability to 0.5. Observe the growth in the displayed chance error by trying 50 tosses, then 100, 500, 1000, and so on. Notice that, as you increase the number of tosses, the chance error grows but the percentage of heads is likely to remain close to 50%. This is the Law of Averages.
Manufacturing Defects
Suppose you are observing a manufacturing process that produces a defective item 5% of the time. You are interested in how often the process will produce two defective items in a row. When this event occurs, the quality control procedures may require the entire manufacturing process to be shut down and inspected.
This process is really just coin tossing in disguise. Set the probability of heads to 0.05, let the longest run equal 2, and press Start to see what happens. Repeat this experiment several times to get an idea of how long it usually takes to observe two defective in a row.
The NBA Foul Line
Your favorite NBA basketball player makes 90% of his free throws. His goal is to make at least 50 free throws in a row during the season. It is not unusual for some of the best players to have more than 300 free throw attempts in a single season. Do you think a goal of 50 in a row is reasonable?
Run the Coin Tossing manipulative with probability of heads set at 0.90 and the longest run of heads set at 50. How many attempts are necessary? Repeat this experiment several times to get an idea of how likely it is that 50 in a row will occur during an entire NBA season.