Elements of combinatorics. Combinatorics

Basic concepts

• random event -
• - this is an event that may occur (occur) or not occur as a result of this experiment.
• Event designations: A, B, C,… , ω ,…
• Example 1. Tossing a coin.
• A \u003d (falling out of the coat of arms)
• B=( loss of digital inscription )

Basic concepts

• Example 2. Throwing a dice .
• =(drop number 1)
• =(drop number 2)
• - - - - - - - - - - - - - - - - -
• =(drop number 6)
• A \u003d (drawing an even number)
• B = (rolling a number less than 4)
• - - - - - - - - - - - - - - - -

Basic concepts

• Consider the set of all events that may or may not occur in this experiment.
• An impossible event is an event that
• cannot occur in this experiment - Ǿ .
• A certain event is an event that will definitely occur in this experiment - Ω .

Basic concepts

• Example 2. Throwing a dice.
• =(drop number 1)
• =(drop number 2)
• - - - - - - - - - - - - - - - - -
• =(drop number 6)
• A \u003d (drawing an even number)
• B = (rolling a number less than 4)
• - - - - - - - - - - - - - - - -
• Ǿ =(rolling a number greater than 6)
• Ω = (dropping any number from 1 to 6)

Basic concepts

Actions
with random events
Sum
A+B
Difference
A-B
Work
AB

Basic concepts

• The sum of two events A and B is such an event C=A+B that occurs if and only if at least one of the events A and B occurs.
• The difference between two events A and B is such an event C=A-B that occurs when A occurs and B does not occur.
• The product of two events A and B is such an event C = AB, which occurs if and only if both A and B occur together.

Basic concepts

• Example (Venn diagrams).
• A point is randomly chosen in the square ( a point is randomly thrown into the square ).

A