Definitions [2]
Definition: Probablity
Probability measures the degree of certainty of the occurrence of an event.
Definition: Conditional Probability
The conditional probability of both events A and B over the sample space S is
\[\mathrm{P(A/B)=\frac{P(A\cap B)}{P(B)}}\], where \[B\neq\phi\]
\[\mathrm{P(B/A)=\frac{P(A\cap B)}{P(A)}}\], where \[A\neq\phi\]
Theorems and Laws [1]
Theorem: Bayes' Theorem
If B1, B2,..., Bn are mutually exclusive and exhaustive events and if A is an event consequent to these Bi's, then for each i = 1, 2, 3, ..., n,
\[\mathrm{P(B_i/A)=\frac{P(B_i)P(A/B_i)}{\sum_{i=1}^nP(A\cap B_i)}}\]
Key Points
Key Points: Concept of Probability
| No. | Term | Definition |
|---|---|---|
| 1 | Probability | A measure of the chance of occurrence of an event. |
| 2 | Random Experiment | An experiment in which all possible outcomes are known, but the exact outcome cannot be predicted with certainty. |
| 3 | Outcome | The result of a random experiment. |
| 4 | Sample Space (S) | The set of all possible outcomes of a random experiment. |
| 5 | Sample Point | Each element of the sample space. |
| 6 | Number of Sample Points | The number of elements in the sample space is denoted by n(S). |
| 7 | Equally Likely Outcomes | Outcomes which have the same chance of occurring. |
Key Points : Standard Sample Space
| No. | Term | Definition |
|---|---|---|
| 1 | Probability | A measure of the chance of occurrence of an event. |
| 2 | Random Experiment | An experiment in which all possible outcomes are known, but the exact outcome cannot be predicted with certainty. |
| 3 | Outcome | The result of a random experiment. |
| 4 | Sample Space (S) | The set of all possible outcomes of a random experiment. |
| 5 | Sample Point | Each element of the sample space. |
| 6 | Number of Sample Points | The number of elements in the sample space is denoted by n(S). |
| 7 | Equally Likely Outcomes | Outcomes which have the same chance of occurring. |
Playing Cards – Key Facts
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Total cards = 52
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Red cards = 26 (Hearts, Diamonds)
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Black cards = 26 (Clubs, Spades)
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Each suit has 13 cards
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Face cards = King, Queen, Jack (Total = 12)
