Conditional Probability · Independent Events

Lesson 2

Nikolai Chukhin · Alexander S. Kulikov

Problem. In this problem, the deck refers to a standard set of 52 cards (4 suits of 13 values, namely 2-10, J, Q, K, A). For each case, determine whether the given pair of events is independent.

5 points

  1. “A randomly selected card from the deck is of the hearts suit” and “A randomly selected card from the deck is a “picture” card (i.e., jack, queen, or king)”.

  2. “Two randomly selected cards from the deck are both black” and “Two randomly selected cards form a pair (i.e., have the same value)”.

  3. “A randomly selected card from the deck is a ten” and “A randomly selected card from the deck is a jack”.

  4. “Among a randomly selected pair of cards, at least one is of the hearts suit” and “Among a randomly selected pair of cards, at least one is an ace”.

  5. “A randomly selected pair of cards from the deck consists of different suits” and “Among a randomly selected pair of cards, at least one is a “picture” card”.