Bayes' Theorem
Chapter Name : Probability |
Sub Topic Code : 104_12_13_05_01 |
Topic Name : Bayes' Theorem |
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Sub Topic Name : Partition Of A Sample Space |
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Introduction
• The events form a partition of sample space if • All events are disjoint. • Intersection of events is empty set. • Union of all events is equal to sample space.
Pre-Requisites:
• Knowledge of events in probability. • Knowledge of set theory.
Activity:
You will observe that average test scores form partition of sample space number of students, by applying theorem of probability we can find overall average test scores.
Real Life Question:
An insurance company divides people into two classes, one is accident prone and the other is non-accident prone. The statistics shows that person having an accident in a fixed time period of one year has a probability of 0.4 and this probability reduces to 0.2 for non-accident person. What is the probability that a new policy holder will have an accident within one year time period?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Probability | Probability is the chance that something will happen. |
| Event | An event is a set of outcomes to which a probability is assigned. An event is subset of sample space. |
| Sample space | Sample space is an exhaustive list of all possible outcomes of an experiment. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Test score marks | Collect test results of three classes of your standard. Class Average Test score Number of students 1 30 20 2 50 30 3 80 10 How to find overall average test scores for all the students. |
Real life uses :
Probability theory is applied for risk assessment in trade or financial markets.
Places to visit :
Suppose you have homework to do, the probabilities that there will be electricity cut off is 0.65 , 0.80 that the homework will be completed on time if there is no electricity problem and 0.32 that the work will be completed on time if there is electricity problem. Determine the probability that the work will be completed on time.(Apply partition rule)
Practical examples around us
| Examples | Explainations |
|---|---|
| Computer set quality | A company that manufactures computer performs quality check on each appliance before packing and shipping. Quality check has an evaluation of picture and appearance. Each of the evaluations is graded as Perfect, Good, Satisfactory, and Fail. We can apply partition rule of probability to find probability values of computer set. |
What you learn in Theory:
If all events are disjoint, and intersection of events is empty and union of events form a sample space then the space is called as partition sample space.
What you learn in Practice:
Sometimes direct computation of probability of an event is not easy so we can break up our sample space into disjoint pieces, compute the probability of an event of each piece and find overall probability of the event.