Election Predictions and Polling Statistics
#COIN FLIP CHOICE SERIES#
This is a transcript from the video series Understanding the Misconceptions of Science. That is still not a good enough measurement to determine if the coin wasn’t unfair by 51 to 49 percent. Even if the coin is flipped 1000 times, you can still expect to get a number in the 47 to 53% range. If a coin is flipped 10 times, the outcome can be anything from 0 to 10 heads. So what’s the message here? The message is that using statistics doesn’t easily answer a question. What if the same experiment is done by flipping the coin 1000 times? If you flip a coin 1000 times, it’s most likely that you’ll get heads somewhere between 47 and 53 percent of the times. So, if you do flip a coin 10 times and see 3 heads, that’s a pretty common outcome and you can’t conclude that the coin is unfair. It shows that when you flip a fair coin 10 times, you can pretty much get any outcome with reasonable probability. (Image: Peter Hermes Furian/Shutterstock) The probability of getting heads clusters closer around the 50% mark as the number of tosses increases. For 6 through 10 heads, it’s just the opposite.
How often can you expect to get heads if you flip a fair coin 10 times? You expect to get 0 heads about 0.1% of the time, 1 head about 1% of the time, 2 heads about 4% of the time, 3 heads about 12% of the time, 4 heads about 21% of the time, and finally, 5 heads only 25% of the time. So, is the coin fair? Well, the conclusion is “maybe”. Say you flipped the coin 10 times and came up with 3 heads. The first question we want to ask is: Is the coin fair? Will you get heads 50% of the time? Let’s start with a situation that’s pretty easy.
(Image: Gearstd/Shutterstock) Judging the Fairness of a Coin But why does this happen? Figuring out percentages and probabilities is a complex task, and one which can lead to misconceptions. By Don Lincoln, Ph.D., University of Notre Dame Percentages are often misleading, even in the simplest of situations, like flipping a coin, and definitely in more complex situations, like poll figures before an election.
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