Let A1,A2,A3,,An be events. Show that if P[A1] = P[A2] = ... = P[An] = 1, then P

Question

Let A1,A2,A3,,An be events. Show that if P[A1] = P[A2] = ... = P[An] = 1, then P[A1A...An] = 1. Is this still true if the collection of events is countably infinite? Is this still true if the collection of events is uncountably infinite? Hint: Consider the complementary events. Let A1,A2,A3,,An be events. Show that if P[A1] = P[A2] = ... = P[An] = 1, then P[A1A...An] = 1. Is this still true if the collection of events is countably infinite? Is this still true if the collection of events is uncountably infinite? Hint: Consider the complementary events.

Explanation / Answer

Ans:

A1 ,A2,A3.......An are independent events,then

P[A1A2A3...An]=P[A1]*P[A2]*P[A3]......P[An]

=1*1*1*1*....1

=1

Yes,it is true even when the  collection of events is uncountably infinite.

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.