Example of events satisfying some conditions

Question

Provide an example of three events A,B,C such that P(A∩B∩C) = P(A)P(B)P(C),P(A∩B) = P(A)P(B),P(A∩C) = P(A)P(C) and P(B∩C) ≠ P(B)P(C).

Answer 1

P(A∩B∩C) = P(A)P(B)P(C)

Three independent events - the result of flipping a coin, rolling a specific number on a die, picking a certain card from a deck

P(A∩B) = P(A)P(B)

Two independent events - the result of flipping a coin, rolling a specific number on a die

P(A∩C) = P(A)P(C)

Two independent events - the result of flipping a coin, picking a certain card from a deck

P(B∩C) ≠ P(B)P(C)

Two dependent events - drawing specific two cards from a deck when drawing without replacement, e.g., draw a king, then draw a queen.