The sample space is an important concept in probability and inferential statistics, as it provides a framework for examining the outcome of events. It is defined as the set of all possible outcomes for any given experiment or trial. In this case, we are looking at the outcomes of two coins being thrown and each showing either a head or a tail. This means that our sample space consists of four possible results: (H, H), (H, T), (T, H), and (T, T).

These four possible results can be broken down into 16 separate events. There are eight different combinations in which both coins show heads: HH-HH; HH-HT; HT-HH; HT-HT; TH-HH; TH-HT; TT-HH; and TT-HT. There are also eight different combinations in which one coin shows heads while the other shows tails: HH-TH; HH-TT; HT-TH ; HT–TT ; TH–HH ; TH–HT ; TT–HH ; and TT–HT.

Describe the sample space and all 16 events for a trial in which two coins are thrown and each shows either a head or a tail.

In summary, when throwing two coins there is a total sample size of 4 possibilities and 16 individual events that could occur with each combination having an equal chance to happen. Each event represents one unique combination out of the four potential results: Heads/Heads (H/H) , Heads/Tails (H/T), Tails/Heads(T/H) ,and Tails /Tails(T/T).