8. Flipping coins and the binomial distribution

Consider two coins, one fair and one unfair. The probability of getting heads on a given flip of the unfair coin is 0.75. You are given one of these coins and will gather information about your coin by flipping it. Based on your flip results, you will infer which of the coins you were given. At the end of the question, which coin you were given will be revealed.

When you flip your coin, your result is based on a simulation. In a simulation, random events are modeled in such a way that the simulated outcomes closely match real-world outcomes. In this simulation, each flip is simulated based on the probabilities of obtaining heads and tails for whichever coin you were given. Your results will be displayed in sequential order from left to right.

Here's your coin! Flip it 10 times by clicking on the red FLIP icons:

What is the probability of obtaining exactly as many heads as you just obtained if your coin is the unfair coin?

0.0021

0.0321

0.0069

0.2503

What is the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin?

0.0069

0.0321

0.1172

0.0021

When you compare these probabilities, it appears more likely that your coin is the coin.

If you flip a fair coin 10 times, what is the probability of obtaining as many heads as you did or greater?

0.7769

0.1719

0.5234

0.1426

The probability you just found is a measure of how unusual your results are if your coin is fair. A low probability (0.10 or less) indicates that your results are so unusual that it is unlikely that you have the fair coin; thus, you can infer that your coin is unfair.

On the basis of this probability, you infer that your coin is unfair.

Click hereto find out whether you were flipping the fair coin or the unfair coin.