Question

Hello,

There is an example in my probability textbook that asks us to calculate the probability of throwing exactly two heads in three tosses using a balanced coin. The reasoning the textbook uses is written below, but our professor wants us to criticize their reasoning, stating that it is a common mistake seen in introductory probability textbooks.

They argue that just because the coin is balanced, each outcome (the result of three tosses) must have probability 1/8. Note that a coin is balanced if P(H)=P(T)=.5 at each toss. It is enough to criticize the reasoning by considering just a two-toss experiment, for which the textbook would (incorrectly) argue that the probability of each pair of outcomes is automatically 1/4, from the fairness of the coin alone.

I am unsure of how to criticize this example. Could someone please provide an explanation?

Thanks

Answer 1