Define Probability and state its Axioms.

You're on a roll — Step 1: Define Probability and state its Axioms. a) Probability* is a numerical measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The Axioms of Probability (Kolmogorov's Axioms) are: 1. Non-negativity: For any event A, the probability of A is non-negative. P(A) 0 2. Normalization: The probability of the sample space S (the set of all possible outcomes) is 1. P(S) = 1 3. Countable Additivity: For any sequence of mutually exclusive events A_1, A_2, A_3, (events that cannot occur at the same time), 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) + Step 2: Write short notes on the given terms. b)* i) An Experiment* is any process that yields an observation or an outcome. For example, tossing a coin or rolling a die. ii) A Sample Space* (S) is the set of all possible outcomes of a random experiment. For example, when rolling a die, S = \1, 2, 3, 4, 5, 6\. iii) An Event Space (or simply an Event*) is a subset of the sample space, consisting of one or more outcomes. For example, rolling an even number on a die is an event E = \2, 4, 6\. iv) A Sample Point* is an individual outcome in the sample space. For example, when rolling a die, '3' is a sample point. v) Trials* are individual repetitions of an experiment. For example, if you toss a coin 10 times, each toss is a trial. Step 3: Calculate the probability of not getting a perfect square. c)* When a fair die is tossed once, the sample space is S = \1, 2, 3, 4, 5, 6\. The total number of possible outcomes is 6. The perfect squares in this sample space are \1, 4\. Let A be the event that a perfect square shows up. The number of outcomes in event A is 2. The probability of event A is: P(A) = Number of perfect squaresTotal number of outcomes = (2)/(6) = (1)/(3) The probability that a perfect square did not show up is P(A'), which is 1 - P(A). P(A') = 1 - P(A) = 1 - (1)/(3) = (2)/(3) The probability that a perfect square did not show up is (2)/(3). What's next?