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(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...") |
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<li><math>\Omega</math> must have at least <math>2n</math> points.</li> | <li><math>\Omega</math> must have at least <math>2n</math> points.</li> | ||
</ul> | </ul> | ||
'''References''' | |||
{{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}} | |||
Revision as of 11:01, 21 June 2024
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.
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.