Definitions [1]
Definition: Probablity
Probability measures the degree of certainty of the occurrence of an event.
Formulae [3]
Formula: Classical (Theoretical) Probability
\[P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}\]
Formula: Empirical (Experimental) Probability
Empirical Probability = $$\frac{\text{Number of times the event occurs}}{\text{Total number of trials}}$$
Formula: Probability of an Event
\[P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}\]
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)
Key Points: Types of Events in Probability
| Type of Event | Meaning | Probability |
|---|---|---|
| Sure (Certain) Event | An event that is certain to occur | P(E) = 1 |
| Impossible Event | An event that cannot occur | P(E) = 0 |
| Simple (Elementary) Event | An event having only one outcome | P(E) = 1 / n(S) |
| Complementary Event (E̅) | An event that occurs when E does not occur | P(not E) = 1 − P(E) |
| Mutually Exclusive Events | Two events that cannot occur together | P(A ∩ B) = 0 |
| Exhaustive Events | Events which together cover all outcomes of S | P(A₁) + P(A₂) + … = 1 |
| Equally Likely Events | All outcomes have the same chance of occurring | P(E) = n(E) / n(S) |
| General Rule | Probability of any event | 0 ≤ P(E) ≤ 1 |
Key points: Standard Results
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Tossing a coin n times or tossing n coins simultaneously gives
Total outcomes = 2n -
Rolling a die n times or rolling n dice simultaneously gives
Total outcomes = 6n
