3.3 Interactive coin toss

In the example below, there are two tree diagrams. The probability tree displays the degree of belief for the coin toss in terms of the probabilities for the outcomes. The expected frequency tree displays the expected number of heads and tails corresponding to those probabilities for a fixed number of coin tosses.

Use the sliders below to change the probability of heads for the coin toss and also the number of tosses with which to view the expected outcomes. Firstly, fix the probability of heads to 0.5, since this is what we did in the example above. Then change the number of tosses to see that the expected number of heads and tails are equal. Next, fix the probability of heads to another number and see how this affects the expected outcomes. The expected frequency tree in the example above shows what the probability model expects to occur for a specified probability of a head. It does not necessarily show what will be observed in practice because there is an unavoidable uncertainty about the outcomes (aleatory uncertainty). Tossing the coin, observing the outcomes, and then using that to refine the probability model falls into the realm of statistics, which is not covered in this book. Interactive examples exploring this topic can be found in our online application.