Revision as of 02:15, 20 June 2024 by Admin (Created page with "Suppose you are given the following: #<math>A_1, A_2, \ldots,A_n</math> are independent events defined on a sample space <math>\Omega</math> # <math>0 < P(A_j) < 1</math> for all <math>j</math> Which of the following statements is always true? <ul class="mw-excansopts"> <li><math>\sum_{i=1}^n P(A_i) < P(A_1 \cup \cdots \cup A_n)</math></li> <li><math>\sum_{i=1}^n P(A_i) = P(A_1 \cup \cdots \cup A_n)</math></li> <li><math>\sum_{i=1}^n P(A_i) < 1</math></li> <li...")
Jun 20'24
Exercise
Suppose you are given the following:
- [math]A_1, A_2, \ldots,A_n[/math] are independent events defined on a sample space [math]\Omega[/math]
- [math]0 \lt P(A_j) \lt 1[/math] for all [math]j[/math]
Which of the following statements is always true?
- [math]\sum_{i=1}^n P(A_i) \lt P(A_1 \cup \cdots \cup A_n)[/math]
- [math]\sum_{i=1}^n P(A_i) = P(A_1 \cup \cdots \cup A_n)[/math]
- [math]\sum_{i=1}^n P(A_i) \lt 1[/math]
- [math]\Omega[/math] must have at least [math]2^n[/math] points.
- [math]\Omega[/math] must have at least [math]2n[/math] points.