Suppose you are given the following:

1. [math]A_1, A_2, \ldots,A_n[/math] are independent events defined on a sample space [math]\Omega[/math]
2. [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.

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.