Probability Theory and Combinatorics - Key Facts and Definitions

An event that always occurs in every trial is called ________.

• Certain (sure) event.

• Impossible event.

• Random event.

• Unlikely event.

The classical definition of probability was given by ________.

• Pierre-Simon Laplace.

• Isaac Newton.

• Blaise Pascal.

• Carl Friedrich Gauss.

The union of events A and B means ________.

• A or B or both occur.

• Only A occurs.

• Only B occurs.

• Neither A nor B occurs.

The intersection of events A and B means ________.

• Both A and B occur simultaneously.

• Only A occurs, not B.

• Only B occurs, not A.

• Either A or B occurs, but not both.

The difference of events A and B (A \ B) means ________.

• A occurs but B does not.

• Both A and B occur.

• B occurs but A does not.

• Neither A nor B occurs.

Combinatorics is ________.

• The branch of mathematics that studies counting, arrangement, and selection of elements.

• A type of geometric transformation.

• A method for solving differential equations.

• A branch of mathematics focused on calculus.

The main problems of combinatorics are related to ________.

• Permutations, placements, and combinations.

• Algebraic equations and inequalities.

• Geometric constructions and proofs.

• Calculus and differential equations.

An example of a combinatorial problem is ________.

• Counting the number of possible passwords.

• Solving a quadratic equation.

• Drawing a straight line.

• Measuring temperature.

For mutually exclusive events A and B, the probability of their union equals ________.

• P(A ∪ B) = P(A) + P(B).

• P(A ∪ B) = P(A) × P(B).

• P(A ∪ B) = P(A) - P(B).

• P(A ∪ B) = P(A) / P(B).

Events that exclude each other’s occurrence are ________.

• Mutually exclusive events.

• Independent events.

• Complementary events.

• Simultaneous events.