Events and Probability Spaces · Events and Probability Spaces

Lesson 3

Nikolai Chukhin · Alexander S. Kulikov

Problem. Mark the correct statements:

5 points

  1. For any event \(A \subseteq U\), it holds that \(0 \le \Pr[A] \le 1\).

  2. \(\Pr[\varnothing]=0\), \(\Pr[U]=1\).

  3. For any event \(A \subseteq U\), it holds that \(\Pr[A]+\Pr[U \setminus A]=1\).

  4. For any events \(A,B \subseteq U\), it holds that \(\Pr[A \cap B]=\Pr[A]+\Pr[B]\).

  5. For any events \(A,B \subseteq U\), it holds that \(\Pr[A \cap B] \le \Pr[A]+\Pr[B]\).

  6. For any events \(A,B \subseteq U\), it holds that \(\Pr[A \cup B] = \Pr[A]+\Pr[B]-\Pr[A \cap B]\).