a) What is Probability? State the Axioms of Probability. b) Write short notes on the following: i) Experiment ii) Sample Space iii) Event Space iv) Sample Point v) Trials. c) If a fair die is tossed once, what is the probability that a perfect square did not show up?

Here are the answers to questions 1.a) and 1.b). I previously solved 1.c) for you. 1. a) What is Probability? State the Axioms of Probability Probability is a numerical measure of the likelihood of an event occurring. It quantifies uncertainty, assigning a value between 0 (impossible) and 1 (certain) to the chance of a specific outcome. The Axioms of Probability are fundamental rules that all probabilities must satisfy. For a sample space S and an event A: 1. Non-negativity: The probability of any event is a non-negative real number. P(A) 0 2. Normalization: The probability of the entire sample space (the event that something happens) is 1. P(S) = 1 3. Additivity (for mutually exclusive events): If A_1, A_2, A_3, are a sequence of mutually exclusive events (meaning no two events can occur at the same time), then the probability of their union is the sum of their individual probabilities. P(A_1 A_2 A_3 ) = P(A_1) + P(A_2) + P(A_3) + 1. b) Write short notes on the following: i) Experiment: An experiment is any process or procedure that yields an observable outcome. In probability, the outcome is uncertain before it is performed, but the set of all possible outcomes is known. ii) Sample Space: The sample space (S) is the set of all possible outcomes of a random experiment. Each element in the sample space is a unique and distinct outcome. iii) Event Space: An event space (or event set) is a subset of the sample space, consisting of one or more outcomes that share a common characteristic. It represents a specific collection of outcomes of interest from an experiment. iv) Sample Point: A sample point is an individual outcome or element in the sample space of a random experiment. It is the most basic possible result of an experiment. v) Trials: A trial refers to a single performance of a random experiment. Each trial results in one specific outcome from the sample space. What's next? Send it over!