Probability Concepts

Probability Concepts- Basic probability concepts and terminology is discussed below

• Probability – It is the chance that something will occur. It is expressed as a decimal fraction or a percentage. It is the ratio of the chances favoring an event to the total number of chances for and against the event. The probability of getting 4 with a rolling of dice, is 1 (count of 4 in a dice) / 6 = .01667. Probability then can be the number of successes divided by the total number of possible occurrences. Pr(A) is the probability of event A. The probability of any event (E) varies between 0 (no probability) and 1 (perfect probability).
• Sample Space – It is the set of possible outcomes of an experiment or the set of conditions. The sample space is often denoted by the capital letter S. Sample space outcomes are denoted using lower-case letters (a, b, c . . .) or the actual values like for a dice, S={1,2,3,4,5,6}
• Event – An event is a subset of a sample space. It is denoted by a capital letter such as A, B, C, etc. Events have outcomes, which are denoted by lower-case letters (a, b, c . . .) or the actual values if given like in rolling of dice, S={1,2,3,4,5,6}, then for event A if rolled dice shows 5 so, A ={5}. The sum of the probabilities of all possible events (multiple E’s) in total sample space (S) is equal to 1.
• Independent Events – Each event is not affected by any other events for example tossing a coin three times and it comes up “Heads” each time, the chance that the next toss will also be a “Head” is still 1/2 as every toss is independent of earlier one.
• Dependent Events – They are the events which are affected by previous events like drawing 2 Cards from a deck will reduce the population for second card and hence, it’s probability as after taking one card from the deck there are less cards available as the probability of getting a King, for the 1st time is 4 out of 52 but for the 2nd time is 3 out of 51.
• Simple Events – An event that cannot be decomposed is a simple event (E). The set of all sample points for an experiment is called the sample space (S).
• Compound Events – Compound events are formed by a composition of two or more events. The two most important probability theorems are the additive and multiplicative laws.
• Union of events – The union of two events is that event consisting of all outcomes contained in either of the two events. The union is denoted by the symbol U placed between the letters indicating the two events like for event A={1,2} and event B={2,3} i.e. outcome of event A can be either 1 or 2 and of event B is 2 or 3 then, AUB = {1,2}
• Intersection of events – The intersection of two events is that event consisting of all outcomes that the two events have in common. The intersection of two events can also be referred to as the joint occurrence of events. The intersection is denoted by the symbol ∩ placed between the letters indicating the two events like for event A={1,2} and event B={2,3} then, A∩B = {2}
• Complement – The complement of an event is the set of outcomes in the sample space that are not in the event itself. The complement is shown by the symbol ` placed after the letter indicating the event like for event A={1,2} and Sample space S={1,2,3,4,5,6} then A`={3,4,5,6}

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