1. Theory of Conditional Probability
Conditional, as the name suggests, is the instance of one incident happening in the event of another one having occurred previously, is applied to Probability and is called Conditional Probability, when the chances of an event occurring is speculated when another event has already occurred. This is one of the most important statistical techniques which denote the manner in which an event will incur some of the similarities of the already occurred event.
For calculating the Conditional Probability, the probability of the previous or already occurred event is multiplied by the probability of the present event or the event which is occurring.
Conditional Probability is unpredictable and depends purely on chance. For example, if we throw a dice of different colors, then the probability of getting one type of color is one-fourth, if there are four types of colors. This concept of chance or contingent nature of Conditional Probability makes it the most unpredictable concept and it entirely depends on unforeseeable circumstances.
There are several types of Conditional Probabilities. Some are independent events, in the sense that the occurrence of one event will not depend on another. In this case, the past event will have little influence on the current occurrence. For example, in tossing a coin there are equal chances for both heads and tails to appear, irrespective of which would have appeared in the previous toss, meaning that both heads and tails stand an equal chance of occurrence.
Some are dependent events, meaning that their probability depends on the occurrence of the previous events therefore, they are called dependent. For example, if there are three marbles each of blue and green color and if one is removed from the bag, the chances of getting another marble at random will change. Thus, it is dependent on the previous chance.
If for instance, we tend to replace the marble taken out, then the probability becomes independent, while if the marble is not replaced, then it takes the case of dependent probability.
When there are two variables X and Y, then the probability or chance of getting X is denoted as P (X) while the probability or chance of acquiring Y is indicated as P (Y). If there are only two variables, then P (X) stands fifty per cent chance of occurring in any event, while that of P(Y) is also fifty per cent. However, if the number of variables varies, then the probabilities or chances of occurrences will also change.
The calculation of probability of any event based on conditional clauses leads to the inclusion of removal of the variable and the change in chance compared to the other forms of probability calculations.
On calculating the probability of both events X and Y, then their total probability will equal to the probability of X multiplied by probability of Y in the event of occurrence of X and is given as follows
P (X and Y) = P (X) x P (Y/X)
Take the instance of 70 per cent of children preferring vanilla flavor in ice cream, while 35 per cent like both chocolate and vanilla. The calculation for the probability of children liking vanilla alone also liking chocolate can be calculated as
P (Chocolate/ Vanilla) = P (Chocolate and Vanilla) / P (Vanilla)
= 0.35 / 0.7 = 50 per cent chance.
Therefore, 50 per cent children who prefer vanilla also like chocolate.
2. Problems encountered in solution to Conditional Probability Problems
Students may find it cumbersome to calculate the probability of values in terms of dependent or independent factors, which involve replacing variables or not replacing variables. This is the primary difficulty faced by many students and which involves careful analysis of the Conditional factors involved in probability.
Also inclusion and exclusion factors play an important role in calculating probability of an event from occurring or recurring.
Chances of an event occurring also depend on dependent and independent variables. In case of dependent variables, they influence the probability or chance of occurrence of any particular event or happening, while independent variables do not wield any influence on the probability or condition of occurrence of any event or incident.
The students should carefully analyze the consequences of possessing the type of conditional probability, whether two factors overlap one another or they behave diversely, which is more demanding of the students and therefore, require them to expect the guidance of an external source.
Also Conditional Probability principles should be studied by students in an extensive manner to become affiliated with the various concepts of the applications of probability. This forms one of the important measures to be taken while solving probability problems.
3. Get help online in Conditional Probability Questions from Statistics experts
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The tutors who are subject matter experts will disseminate information on the topic to the students in a manner that will be easily understood by the students. In addition, the methodology adapted by the tutors will make it feasible for the students to solve the problems with ease and also to find alternate solutions to the same problem in an issueless manner.
The website helps in connecting the tutors and students such that preference is provided to the students' tasks and their work is completed on time. Conditional Probability problems can be solved with utmost simplicity such that the students will get a chance to imbibe the knowledge faster and better when compared to learning the concepts by themselves.
Also interaction with tutors will enable the students become stronger in the foundation of Conditional Probability principles and they will be able to tackle the problems with confidence and grit.
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Therefore, it is vital that students increase their proficiency in Conditional Probability by seeking the guidance and information on the topic from efficient tutors and a reliable website.