a) What is Probability? State the Axioms of Probability. b) Write short notes on the following: i) Experiment…

Question

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?

ScanSolve AI Tutor · Accepted Answer

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 $A$ :

Non-negativity
The probability of any event is a non-negative real number.
$P(A) \ge 0$
Normalization
The probability of the entire sample space (the event that something happens) is 1.
$P(S) = 1$
Additivity (for mutually exclusive events)
If $A_1, A_2, A_3, \dots$ 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.
$P(A_1 \cup A_2 \cup A_3 \cup \dots) = P(A_1) + P(A_2) + P(A_3) + \dots$
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.

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?

Step-by-step solution

Non-negativity

Normalization

Additivity (for mutually exclusive events)

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