The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:
Statistics and probability are two tools of mathematics discipline concerning the collection, organization, processing, and analysis of quantifiable data. Statistics is limited to the aspects of gathering, managing, and interpreting quantifiable data, whereas probability presents predictions about the occurrence or non-occurrence of events in a varied environment. Statistics and probability are very closely linked due to the presence of quantifiable data and interpretation phenomenon. Additionally, these two mathematical tools also help the students in generating support for an argument with persuasive data.
There are two formulas for the addition rule of probability, pertaining to a probability related to two mutually exclusive events and probability related to two non-mutually exclusive events. The first formula is merely the sum of the probabilities of occurrences or non-occurrence in two events, whereas the second formula adds the aspect of deducting the probability of occurrence of both events simultaneously along with adding the probabilities of occurrences or non-occurrences of two events. This concept can also be understood by videos and materials available on MSVgo.
Binomial probability can be defined as the formulae of sourcing the exact number of successes of getting desired results in a specific number of trials. The formulae for calculating the probability of failure using binomial probability is P(F)= 1 – p (where p is the probability of success, and 1 is the total probability of event occurrence). For more information about binomial probability, check informative content on MSVgo.
Bayes’ theorem is used for finding the probability of occurrence or non-occurrence of an event if other probabilities are certain. The formula for this theorem is P(A|B) = P(A) P(B|A)/P(B) where P(A|B) details the time event A happens with event B, P(B|A) details the times the event B happens with event A, P(A) is the likeliness of event A happening and P(B) is the likeliness of event B happening. For more understanding, browse videos on MSVgo.
A compound event is a combination of two or more simple events with multiple outcomes. On the other hand, the compound probabilities are the probabilities of events pertaining to multiple outcomes and desires results within specific trails. The key example of compound probability can be rolling an even number on a dice as it has six possible outcomes out of which three are even; thus, the probability of acquiring 2,4 or 6 on dice can be defined as a compound probability. In other words, the compound probability is the mathematical likeliness of two independent events occurring in a specific environment. Generally, the compound probability is derived by multiplying the probability of first event occurrence with the probability of second event occurrence. However, it is to be noted that the formula for calculating the compound probability tends to differ on the basis of the sort of compound event being mutually exclusive and mutually inclusive. For further clarification on this concept, check videos on MSVgo.
In probability theory, the complement of occurrence of any event is the probability of that event not occurring. For instance, the complement of event A is the event NOT A. Denotation of the complimentary event is A’ or Ac. If event A is it will rain today, the complement event A’ will be; it will not rain today. The commonality among complementary events is that they are mutually exclusive and exhaustive. However, if the events are mutually exclusive, they cannot occur simultaneously; however, as they are exhaustive, the sum of their probabilities needs to be 100%. For more understanding about the concept of complementary events, browse videos on MSVgo.
Conditional probability concerns the probability of occurrence of an event along with a relationship to one or multiple other events. For instance, if event A is of raining outside with a probability of 0.3 and event B is going outside with a probability of 0.5. The conditional probability will be applied when going outside is subjected to raining outside. The formula of conditional probability is P(B|A) = P (A and B) / P(A) or P(B|A) = P(A∩B) / P(A). Conditional probability is generally used in the diversified fields of calculus, politics, and insurance. This concept can also be understood by videos and materials available on MSVgo.
When a coin is flipped, there are two possible outcomes, which are either head or tail, with a 50 percent probability for each. The probability for the occurrence of the head on top or tail on top when a coin is flipped is always 50-50 due to the presence of only two alternatives. For more information and questions related to coin toss probability, browse the videos on MSVgo.
Statistics and probability are the two branches of mathematics that are concerned with practices that govern occurrences and non-occurrences of random events by means of collecting, analyzing, interpreting, and presenting numerical data in an efficient way. Probability provides the logic of uncertainty for predicting events so that actions can be taken accordingly in real-time.
What is probability and statistics in math?
Probability and statistics are the branches of mathematics concerned with laws and practices of governing random events by collecting, analyzing, interpreting, and displaying numerical data.
What is the role of probability in statistics?
Probability concerns with conducting an analysis of chances, games, genetics, and predictions pertaining to everyday activities and presenting interpretation in numerical data on the basis of the same.
What is the purpose of probability?
Probability concerns with detailing the likelihood of the occurrence of some event or something in varied aspects such as a game of chances or weather pattern predictions. The likeliness of an event occurring or not occurring tend to help individuals in varied ways.
What are the four types of probability?
Classical, empirical, subjective, and axiomatic are the four types of probability.
What is statistics in math?
Statistics is the branch of mathematics that concerns the collection, analysis, and interpretation of numerical and quantitative data. Statistics presents numeric data using graphs for the easy and efficient understanding of the processing data pertaining to the specific topic, environment, condition, or situation.