In statistics, a **sample space** refers to a set of all possible outcomes that a sample might take. For example, the sample space of a single coin flip contains two possible outcomes: $S=\\{H,T\\}$, while the sample space of two coin flips includes four possible events $S=\\{HH,HT,TH,TT\\}$, the sample space of three coin flips includes eight possible events $S=\\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\\}$, and so on. An **event** refers to whether a particular condition is met for each possible outcome in a sample space. For example, if the sqmpe space for three coin flips is $S=\\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\\}$ and the event of interest is "exactly two tails," then the event is not true of the first four possible outcomes, nor of the last; only three out of eight possible outcomes satisfy this condition, so we would say that the event has occurred only if we observe the fifth, sixth, or seventh possible outcome. The probability of an *event* is equal to the sum of probabilities for all possible outcomes in the *sample space* that satisfy the condition defining that event. If all possible outcomes are equally probable, the probability of the event is equal to the proportion of outcomes that satisfy the condition defining the event out of all possible outcomes. The image [hereJChttps://drive.google.com/file/d/llBDElj1K04rhnTrlhfSQVmeIou M gbC/view?usp=sharing) depicts the map of a six-by-six meter area at a plantation site in the state of Virginia, where a group of 6 archaeologists plan to conduct exploratory excavations. The grid divides the area into 36 one-by-one meter squares, and the team of archaeologists have enough time to excavate one square per person (i.e. six squares in total). The area is covered by grass, with no artifacts or other archaeological remains visible on the surface. However, four of these one-by-one meter squares contain archaeological materials below the surface: storage features (abbreviated \"Feat." on the map) containing caches of farming tools. The team of archaeologists must choose a strategy for picking squares to excavate, in hope of determining how this area of the plantation was used in the past, if at all. For each of the following strategies, do each of the following: (1) Describe the sample space by naming the possible outcomes it contains as well as how many possible outcomes there are. (2) Count how many of these possible outcomes are favorable to the detection of *at least* one feature (i.e., the "event of interest"). (3) Calculate the probability of the event of interest (the proportion of outcomes that are favorable to the event out of all possible outcomes). I (A). A single numbered row is selected at random by rolling a six-sided die; each archaeologist in the team will excavate a different square in that row. *Write the name and number of possible outcomes constituting the sample space. Count the number of possible outcomes that satisfy the condition defining the event of interest. Calculate the probability of this event.* (B). A diagonal series of squares is selected at random by Flipping a coin, either starting with the upper left square (A1, 32, C3, D4, E5, F6) or the lower left square (A6, BS, C4, DB, E2, F1). *Write the name and number of possible outcomes constituting the sample space. Count the number of possible outcomes that satisfy the condition defining the event of interest. Calculate the probability of this event.* (C). a "staggered\" or checkerboard pattern is followed down two adjacent columns, starting at random either at A1, Bl, C1, 01, or E1. For example, if starting at A1, then the pattern is A1, 32, A3, B4, A5, B6. *Write the name and number of possible outcomes constituting the sample space. Count the number of possible outcomes that satisfy the condition defining the event of interest. Calculate the probability of this event.*